No, not every electron absorbed as a photon emerges as a photoelectron.
Do all the electrons that absorb a photon come out as photoelectrons?
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Selina
There are materials which absorb photons of shorter wavelength and emit photons of longer wavelength. Can there be stable substances which absorb photons of larger wavelength and emit light of shorter wavelength?
When the frequency of a photon drops, the wavelength of the photon rises. There are two alternative scenarios: case one, in which the photons have a shorter wavelength and the energy is consumed...
(i) In the explanation of the photoelectric effect, we assume one photon of frequency ν collides with an electron and transfers its energy. This leads to the equation for the maximum energy Emax of the emitted electron as Emax = hν – φ0 where φ0 is the work function of the metal. If an electron absorbs 2 photons (each of frequency ν ) what will be the maximum energy for the emitted electron? (ii) Why is this fact (two-photon absorption) not taken into consideration in our discussion of the stopping potential?
i)According to the question, the electron absorbs two protons with frequencies of v and v'= 2v, where v' is the frequency of the released electron. Emax = hv – ϕ0 ii) There is no emission since the...
A proton and an α-particle are accelerated, using the same potential difference. How are the de Broglie wavelengths λp and λa related to each other?
The proton and α-particle are accelerated at the same potential difference. λ = h/√2mqv λ is proportional to 1/√mq λp/ λa = √maqa/mpqp = √8 Hence, proton wavelength is √8 times α-particle....
A particle moves in a closed orbit around the origin, due to a force which is directed towards the origin. The de Broglie wavelength of the particle varies cyclically between two values λ1, λ2 with λ1>λ2. Which of the following statement are true? (a) The particle could be moving in a circular orbit with origin as centre (b) The particle could be moving in an elliptic orbit with origin as its focus (c) When the de Broglie wavelength is λ1, the particle is nearer the origin than when its value is λ2 (d) When the de Broglie wavelength is λ2, the particle is nearer the origin than when its value is λ1
The correct answers are b) The particle could be moving in an elliptic orbit with origin as its focus d) When the de Broglie wavelength is λ2, the particle is nearer the origin than when its value...
Photons absorbed in matter are converted to heat. A source emitting n photon/sec of frequency ν is used to convert 1kg of ice at 0°C to water at 0°C. Then, the time T taken for the conversion (a) decreases with increasing n, with ν fixed (b) decreases with n fixed, ν increasing (c) remains constant with n and ν changing such that nν = constant (d) increases when the product nν increases
The correct answers are a) decreases with increasing n, with ν fixed b) decreases with n fixed, ν increasing c) remains constant with n and ν changing such that nν = constant
The de Broglie wavelength of a photon is twice the de Broglie wavelength of an electron. The speed of the electron is ve = c/100. Then (a) 
(b)
(c) 
(d) 
The correct answers are b) Ee/Ep = 10-2 c) Pe/mec = 10-2
Two particles A1 and A2 of masses m1, m2 (m1 > m2) have the same de Broglie wavelength. Then (a) their momenta are the same (b) their energies are the same (c) energy of A1 is less than the energy of A2 (d) energy of A1 is more than the energy of A2
The correct answers are a) their momenta are the same c) energy of A1 is less than the energy of A2
Relativistic corrections become necessary when the expression for the kinetic energy 1/2 mv2 , becomes comparable with mc2, where m is the mass of the particle. At what de Broglie wavelength will relativistic corrections become important for an electron? (a) λ =10nm (b)
nm (c) 
nm (d)
nm
The correct answers are c) λ =10–4nm d) λ =10–6nm
An electron is moving with an initial velocity 
and is in a magnetic field 
Then it’s de Broglie wavelength (a) remains constant (b) increases with time (c) decreases with time (d) increases and decreases periodically
The correct answer is a) remains constant
A proton, a neutron, an electron and an α-particle have the same energy. Then their de Broglie wavelengths compare as (a) λp = λn > λe > λα (b) λα < λp = λn < λe (c) λe < λp = λn > λα (d) λe = λp = λn = λα
The correct answer is b) λα < λp = λn < λe
Consider Fig. 11.7 in the NCERT textbook of physics for Class XII. Suppose the voltage applied to A is increased. The diffracted beam will have the maximum at a value of θ that (a) will be larger than the earlier value (b) will be the same as the earlier value (c) will be less than the earlier value (d) will depend on the target
The correct answer is c) will be less than the earlier value
Consider a beam of electrons (each electron with energy E0) incident on a metal surface kept in an evacuated chamber. Then (a) no electrons will be emitted as only photons can emit electrons (b) electrons can be emitted but all with an energy, E0 (c) electrons can be emitted with any energy, with a maximum of E0 – φ (φ is the work function) (d) electrons can be emitted with any energy, with a maximum of E0
The correct answer is d) electrons can be emitted with any energy, with a maximum of E0
The wavelength of a photon needed to remove a proton from a nucleus which is bound to the nucleus with 1 MeV energy is nearly (a) 1.2 nm (b) 
nm (c) 
nm (d)
nm
The correct answer is b) 1.2 × 10–3 nm
A particle is dropped from a height H. The de Broglie wavelength of the particle as a function of height is proportional to (a) H (b) H ½ (c) H0 (d)
The correct answer is d) H–1/2
Lifetimes of the molecules in the excited states are often measured by using pulsed radiation source of duration nearly in the nanosecond range. If the radiation source has the duration of 2 ns and the number of photons emitted during the pulse source is 
, calculate the energy of the source.
Frequency of radiation $\nu$ $\nu =\frac{1}{2.0\times 10^{-9}s}$ $\nu =5.0\times 10^{8}s^{-1}$ Energy (E) of source = Nhν Where, N is the no. photons emitted h is Planck’s constant ν denotes the...
The ejection of the photoelectron from the silver metal in the photoelectric effect experiment can be stopped by applying the voltage of 0.35 V when the radiation 256.7 nm is used. Calculate the work function for silver metal.
The energy associated with an incident photon (E) must equal the sum of its kinetic energy and the work function (W0) of the radiation, according to the rule of conservation of energy. E = W0 + K.E...
If the photon of the wavelength 150 pm strikes an atom and one of its inner bound electrons is ejected out with a velocity of 
, calculate the energy with which it is bound to the nucleus.
Energy of incident photon (E) is given by, $E=\frac{hc}{\lambda }$ $E=\frac{(6.626\times 10^{-34})(3\times 10^{8})}{(150\times 10^{-12})}=1.3252\times 10^{-15}\, J$ $\simeq 13.252\times 10^{-16}J$...
Emission transitions in the Paschen series end at orbit n = 3 and start from orbit n and can be represented as v = 
(Hz) [1/3^2 – 1/n^ 2 ] Calculate the value of n if the transition is observed at 1285 nm. Find the region of the spectrum.
Wavelength of the transition = 1285 nm =$1285 \times 10^{-9} m$(Given) $\nu =3.29\times 10^{15}(\frac{1}{3^{2}}-\frac{1}{n^{2}})$ Since$ \nu =\frac{c}{\lambda }$ =$\frac{3\times...
Calculate the wavelength for the emission transition if it starts from the orbit having radius 1.3225 nm and ends at 211.6 pm. Name the series to which this transition belongs and the region of the spectrum.
The radius of the n th orbit of hydrogen-like particles is given by, $r=\frac{0.529n^{2}}{Z}$ $r=\frac{5.29n^{2}}{Z}pm$ For radius (r1) = 1.3225 nm $=1.32225\times 10^{-9}m$ $=1322.25\times...
Dual behaviour of matter proposed by de Broglie led to the discovery of electron microscope often used for the highly magnified images of biological molecules and another type of material. If the velocity of the electron in this microscope is 
, calculate de Broglie wavelength associated with this electron.
As per de Broglie’s equation, $\lambda =\frac{h}{m\nu }$ =$\frac{(6.626\times 10^{-34})}{9.103939\times 10^{-31}kg(1.6\times 10^{6}ms^{-1})}$ =$4.55\times 10^{-10}m\lambda =455pm$ Therefore, de...
Similar to electron diffraction, neutron diffraction microscope is also used for the determination of the structure of molecules. If the wavelength used here is 800 pm, calculate the characteristic velocity associated with the neutron.
From de Broglie’s equation, $\lambda =\frac{h}{m\nu }$ $\nu=\frac{h}{m\lambda}$ Where, v denotes the velocity of the neutron h is Planck’s constant m is the mass of the neutron λ is the wavelength...
If the velocity of the electron in Bohr’s first orbit is 
, calculate the de Broglie wavelength associated with it.
As per de Broglie’s equation, $\lambda =\frac{h}{m\nu}$ Where, λ is the wavelength of the electron h is Planck’s constant m is the mass of the electron v denotes the velocity of electron...
The velocity associated with a proton moving in a potential difference of 1000 V is 
. If the hockey ball of mass 0.1 kg is moving with this velocity, calculate the wavelength associated with this velocity.
As per de Broglie’s expression, $\lambda =\frac{h}{m\nu }$ $ =\frac{(6.626\times 10^{-34})}{0.1kg(4.37\times 10^{5}ms^{-1})}$=$1.516\times 10^{-38}m$
If the position of the electron is measured within an accuracy of ± 0.002 nm, calculate the uncertainty in the momentum of the electron. Suppose the momentum of the electron is h/4πm × 0.05 nm, is there any problem in defining this value.
As per Heisenberg’s uncertainty principle, ∆x.∆p >= h/4π Where, ∆x = uncertainty in the position of the electron ∆p = uncertainty in the momentum of the electron Substituting the given values in...
The quantum numbers of six electrons are given below. Arrange them in order of increasing energies. If any of these combination(s) has/have the same energy lists: n = 4, l = 2, ml = –2 , ms = –1/2 n = 3, l = 2, ml= 1 , ms = +1/2 n = 4, l = 1, ml = 0 , ms = +1/2 n = 3, l = 2, ml = –2 , ms = –1/2 n = 3, l = 1, ml = –1 , ms= +1/2 n = 4, l = 1, ml = 0 , ms = +1/2
The 4d, 3d, 4p, 3d, 3p, and 4p orbitals are home to electrons 1, 2, 3, 4, 5, and 6. (respectively). Ranking these orbitals in the increasing order of energies: (3p) < (3d) < (4p) < (4d).
The bromine atom possesses 35 electrons. It contains 6 electrons in 2p orbital, 6 electrons in 3p orbital and 5 electrons in 4p orbital. Which of these electron experiences the lowest effective nuclear charge?
The nuclear charge that electrons (which are present in atoms containing multiple electrons) feel is determined by the distance between their orbital and the atom's nucleus. The smaller the...
Among the following pairs of orbitals which orbital will experience the larger effective nuclear charge? (i) 2s and 3s, (ii) 4d and 4f, (iii) 3d and 3p
The net positive charge acting on an electron in an atom's orbital with more than one electron is known as the nuclear charge. The distance between the orbital and the nucleus is inversely...
The unpaired electrons in Al and Si are present in 3p orbital. Which electrons will experience more effective nuclear charge from the nucleus?
The net positive charge acting on an electron in an atom's orbital with more than one electron is known as the nuclear charge. The nuclear charge increases as the atomic number increases. Silicon...
Indicate the number of unpaired electrons in: (a)P (b)Si (c)Cr (d)Fe (e)Kr
(a)Phosphorus (P): The atomic number of phosphorus is 15 Electronic configuration of Phosphorus: 1s 2 2s 2 2p 6 3s 2 3p 3 This can be represented as follows: From the diagram, it can be observed...
(a) How many sub-shells are associated with n = 4? (b) How many electrons will be present in the sub-shells having ms value of –1/2 for n = 4?
(a)n = 4 (Given) For some value of ‘n’, the values of ‘l’ range from 0 to (n – 1). Here, the possible values of l are 0, 1, 2, and 3 Therefore, a total of 4 subshells are possible when n=4: the s,...
For your agricultural field or garden you have developed a compost producing pit. Discuss the process in the light of bad odour, flies and recycling of wastes for a good product.
To avoid odours and insects, the compost pit should be covered. To avoid interfering with the breakdown of the wastes, non-biodegradable wastes should not be thrown into the compost pit. They should...
How can domestic waste be used as manure?
To begin, trash must be separated into biodegradable and non-biodegradable categories. Biodegradable materials, such as leaves and food wastes, are deposited in landfills alongside microorganisms...
A large number of fish are suddenly found floating dead on a lake. There is no evidence of toxic dumping but you find an abundance of phytoplankton. Suggest a reason for the fish kill.
Bacteria eat phytoplankton, and this process necessitates the presence of dissolved oxygen. As a result, the greater the number of Phytoplankton present, the greater the consumption of dissolved...
What would have happened if the greenhouse gases were totally missing in the earth’s atmosphere? Discuss.
The greenhouse gases in our atmosphere capture the sun's UV rays and heat up the earth. Without greenhouse gases, the earth will be unable to retain any heat, which is necessary for the existence of...
What do you mean by green chemistry? How will it help decrease environmental pollution?
The manufacturing process employs our current understanding of chemistry principles to produce, develop, and deploy chemical compounds and products that reduce the amount of harmful chemicals in the...
What are pesticides and herbicides? Explain giving examples.
A pesticide is a combination of two or more chemicals that is used to kill bugs. Plant diseases, weeds, insects, mollusks, and other pests that damage plants and cause them to die must all be...
Do you observe any soil pollution in your neighbourhood? What efforts will you make for controlling the soil pollution?
Pesticides and fertilisers are the most common contaminants that pollute soil. Because pesticides like DDT are not soluble in water, they remain in the soil for prolonged periods of time, polluting...
What do you mean by Biochemical Oxygen Demand (BOD)?
The quantity of oxygen required by bacteria to breakdown organic materials in a given volume of water is known as biochemical oxygen demand. A BOD of less than 5 ppm indicates clean water, but a BOD...
Have you ever observed any water pollution in your area? What measures would you suggest to control it?
Water pollution is caused by human activities such as storm-water drainage, run-off from agricultural areas, wastewater treatment plant emissions, and so on. Industries and factories emit toxic...
What are the major causes of water pollution? Explain.
Water pollution happens when undesired and unwanted chemicals are introduced into water bodies, suffocating the aquatic life that lives there. The following are the primary sources of water...
What do you mean by ozone hole? What are its consequences?
Polar stratospheric clouds offer a surface for the reaction of hypochlorous acid and chlorine nitrate, which produces molecular chlorine after further reaction. Photolysis of HOCl and Molecular...
What are the reactions involved for ozone layer depletion in the stratosphere?
In the stratosphere, ozone is actually formed by the action of UV rays on Dioxygen molecules(O2). (i) O2(g) →UV O(g) +O(g) (ii) O2(g) + O(g) ↔UV O3(g) The second reaction demonstrates that the...
What are the harmful effects of photochemical smog and how can they be controlled?
Photochemical smog is oxidising in nature because it contains NO2 and O3, which cause rubber, stones, metals, and painted surfaces to corrode. Formaldehyde, PAN, and acrolein are also found in...
Write down the reactions involved during the formation of photochemical smog.
The interaction of sunlight with nitrogen oxides and hydrocarbons produces photochemical smog. The major components of photochemical smog include formaldehyde, nitric oxide, ozone, PAN, and...
What is smog? How is classical smog different from photochemical smogs?
Smog is a combination of smoke and fog which causes air pollution. There are two types of smog: a) Photochemical smog b) Classical smog They can be differentiated as follows: Photochemical smog ...
Statues and monuments in India are affected by acid rain. How?
By interacting with water in the presence of ambient oxygen, nitrogen oxides (NO2, NO) and sulphur oxides (SO2 and SO3) produced by the combustion of coal, car gasoline, and other fossil fuels...
List gases which are responsible for greenhouse effect.
The major gases that cause greenhouse effect are: 1) Chlorofluorocarbons (CFCs) 2) Methane (CH4) 3) Carbon dioxide (CO2) 4) Nitrous oxide (NO) 5) Water(H2O) 6) Ozone (O3)
Carbon monoxide gas is more dangerous than carbon dioxide gas. Why?
Carbon dioxide (CO2) and carbon monoxide (CO) are both produced when various fuels are burned. In nature, carbon monoxide is harmful, but carbon dioxide is non-toxic. Because carbon monoxide forms a...
Explain tropospheric pollution in 100 words.
Tropospheric pollution is caused by the presence of undesirable chemicals in the troposphere's lowest layer. Nitrogen oxides, sulphur oxides, carbon, and hydrocarbons are the most common...
What is the maximum number of emission lines when the excited electron of a H atom in n = 6 drops to the ground state?
A total number of 15 lines (5 + 4 + 3 + 2 + 1) will be obtained in this hydrogen emission spectrum. The total number of spectral lines emitted when an electron drops to the ground state from the...
How much energy is required to ionise a H atom if the electron occupies n = 5 orbit? Compare your answer with the ionization enthalpy of H atom (energy required to remove the electron from n =1 orbit).
The expression for the ionization energy is given by, $E_{n} =\frac{-(2.18\times 10^{-18})Z^{2}}{n^{2}}$ Where Z denotes the atomic number and n is the principal quantum number For the ionization...
What is the wavelength of light emitted when the electron in a hydrogen atom undergoes the transition from an energy level with n = 4 to an energy level with n = 2?
The $n_{i} = 4$ to$ n_{f}$= 2 transition results in a spectral line of the Balmer series. The energy involved in this transition can be calculated using the following expression: $E=2.18\times...
Electrons are emitted with zero velocity from a metal surface when it is exposed to radiation of wavelength 6800 Å. Calculate threshold frequency (ν0 ) and work function (W0 ) of the metal.
Threshold wavelength of the radiation $(\lambda _{0})= 6800 Å=6800\times 10^{-10}\, m$ Threshold frequency of the metal $(\nu _{0}) =\frac{c}{\lambda _{0}}=$ $\frac{3\times 10^{8}ms^{-1}}{6.8\times...
Electromagnetic radiation of wavelength 242 nm is just sufficient to ionise the sodium atom. Calculate the ionisation energy of sodium in
Ionization energy (E) of sodium =$ \frac{N_{A}hc}{\lambda }$ =$\frac{(6.023\times 10^{23}\, mol^{-1})(6.626\times 10^{-34})Js(3\times 10^{8})ms^{-1}}{242\times 10^{-9}m}$ =$4.947\times 10^{5}\, J\,...
A photon of wavelength
m strikes on metal surface, the work function of the metal is 2.13 eV. Calculate (i) the energy of the photon (eV), (ii) the kinetic energy of the emission, and (iii) the velocity of the photoelectron 
.
(i) Energy of the photon $(E)= h\nu =\frac{hc}{\lambda }$ Where, h denotes Planck’s constant, whose value is $6.626\times 10^{-34}\,Js$ c denotes the speed of light =$ 3\times 10^{8}\,m/s$...
What is the number of photons of light with a wavelength of 4000 pm that provides 1J of energy?
Energy of one photon (E) =$ h\nu$ Energy of ‘n’ photons $E_{n} = nh\nu \Rightarrow n=\frac{E_{n}\lambda }$ Where, \lambdaλ is the wavelength of the photons = 4000 pm = $4000\times 10^{-12}\, m$ c...
Calculate the wavelength, frequency and wavenumber of a light wave whose period is 2.0 × 10–10 s.
Frequency of the light wave $\nu$ = $\frac{1}{Period} \frac{1}{Period}$ $=\frac{1}{2.0\times 10^{-10}\, s} =5.0\times 10^{9}\, s^{-1 }$ Wavelength of the light wave$\lambda=c\nu$ Where, c denotes...
Find the energy of each of the photons which (i) correspond to light of frequency 
Hz. (ii) have a wavelength of 0.50 Å.
(i) The energy of a photon (E) can be calculated by using the following expression: $E= h\nu$ Where, ‘h’ denotes Planck’s constant, which is equal to $6.626\times 10^{-34}\, Js\nuν$ (frequency of...
Yellow light emitted from a sodium lamp has a wavelength (λ) of 580 nm. Calculate the frequency (ν) and wavenumber (ν ) of the yellow light.
Rearranging the expression, $\lambda =\frac{c}{\nu }$ the following expression can be obtained, $\nu =\frac{c}{ \lambda }$ ……….(1) Here, $\nu$ denotes the frequency of the yellow light c denotes...
Write the complete symbol for the atom with the given atomic number (Z) and atomic mass (A) (I)Z = 17, A = 35 (II)Z = 92, A = 233 (III)Z = 4, A = 9
(i)\({}_{17}^{35}C\) (ii)\({}_{92}^{233}C\) (iii)\({}_{4}^{9}C\)
How many neutrons and protons are there in the following nuclei? 
\({}_{6}^{13}C\): Mass number of carbon-13 = 13 Atomic number of carbon = Number of protons in one carbon atom = 6 Therfore, total number of neutrons in 1 carbon atom = Mass number – Atomic number =...
(i) Calculate the total number of electrons present in one mole of methane. (ii) Find (a) the total number and (b) the total mass of neutrons in 7 mg of 14C. (Assume that mass of a neutron = 1.675 × 10–27 kg). (iii) Find (a) the total number and (b) the total mass of protons in 34 mg of NH3 at STP. Will the answer change if the temperature and pressure are changed?
(i) 1 molecule of methane contains 10 electrons (6 from carbon, 4 from hydrogen) Therefore, 1 mole of methane contains 10*NA = 6.022*1024 electrons. (ii) Number of neutrons in 14g (1 mol) of 14C =...
(i) Calculate the number of electrons which will together weigh one gram. (ii) Calculate the mass and charge of one mole of electrons.
1 electron weighs 9.109*10-31 kg. Therefore, number of electrons that weigh 1 g (10-3 kg) = 1.098*1027 electrons (ii) Mass of one mole of electrons = NA* mass of one electron =...
Dinitrogen and dihydrogen react with each other to produce ammonia according to the following chemical equation: N2 (g) + H2(g)→ 2NH3 (g) (i) Calculate the mass of 
produced if 
g 
reacts with 
g of 
? (ii) Will any of the two reactants remain unreacted? (iii) If yes, which one and what would be its mass.
(i) Balance the given equation: $N_{ 2 }\;(g) \; + \; 3H_{ 2 } \;(g) \; \rightarrow \; 2NH_{ 3 }\;(g) $ Thus, 1 mole (28 g) of N2 reacts with 3 mole (6 g) of H2 to give 2 mole (34 g)...
How are 0.50 mol 
and 0.50 M different?
Molar mass of $Na_{ 2 }CO_{ 3 }$ = (2 × 23) + 12 + (3 × 16) = $106 g mol^{ -1 }$ 1 mole of $Na_{ 2 }CO_{ 3 }$ means 106 g of $Na_{ 2 }CO_{ 3 }$ Therefore, 0.5 mol of $Na_{ 2 }CO_{ 3 }$...
If 10 volumes of dihydrogen gas reacts with five volumes of dioxygen gas, how many volumes of water vapour would be produced?
2H2(g) +O2(g) →2H2O(g) 2 volumes of dihydrogen react with 1 volume of dioxygen to produce two volumes of vapour. Hence, 10 volumes of dihydrogen will react with five volumes of dioxygen to...
Convert the following into basic units: (i) 28.7 pm (ii) 15.15 pm (iii) 25365 mg
(i) 28.7 pm $1 pm = 10^{ -12 } \; m$ $28.7 pm = 28.7 \times 10^{ -12 } \; m$ $= 2.87 \times 10^{ -11 } \; m$ (ii) 15.15 pm $1 pm = 10^{ -12 } \; m$ $15.15 pm = 15.15 \times 10^{ -12 } \; m$...
Which one of the following will have the largest number of atoms? (i) 1 g Au (s) (ii) 1 g Na (s) (iii) 1 g Li (s) (iv) 
(g)
(i) 1 g Au (s) = $\frac{ 1 }{ 197 }$ mol of Au (s) = $\frac{ 6.022 \; \times \; 10^{ 23 } }{ 197 }$ atoms of Au (s) = $3.06 \times \; 10^{ 21 }$ atoms of Au (s) (ii) 1 g Na (s) = $\frac{ 1...
Calculate the molarity of a solution of ethanol in water, in which the mole fraction of ethanol is 0.040 (assume the density of water to be one).
Mole fraction of $C_{ 2 }H_{ 5 }OH$ = $\frac{Number \; of \; moles \; of \; C_{ 2 }H_{ 5 }OH}{Number \; of \; moles \; of \; solution}$ $0.040 = \frac{n_{C_{ 2 }H_{ 5 }OH}}{n_{C_{ 2 }H_{ 5 }OH} \; +...
What will be the mass of one 
atom in g?
1 mole of carbon atoms =$ 6.023 \; \times \; 10^{ 23 }$atoms of carbon = 12 g of carbon Therefore, mass of $1 _{}^{ 12 }\textrm{ C }$ atom = $\frac{ 12 \; g }{ 6.022 \; \times \; 10^{ 23 }}$...
How many significant figures should be present in the answer of the following calculations? (i)
(ii) 5 × 5.365 (iii) 0.012 + 0.7864 + 0.0215
(i) $\frac{ 0.02856 \; \times \; 298.15 \; \times \; 0.112}{ 0.5785 }$ Least precise no. of calculation = 0.112 Therefore, no. of significant numbers in the answer = No. of significant numbers in...
Use the data given in the following table to calculate the molar mass of naturally occurring argon isotopes:
Molar mass of Argon: =$ [( 35.96755 \; \times \; \frac{ 0.337 }{ 100 }) + ( 37.96272 \; \times \; \frac{ 0.063 }{ 100 })+ ( 39.9624 \; \times \; \frac{ 99.600 }{ 100 })]$ =$ [0.121 + 0.024 + 39.802]...
Calculate the number of atoms in each of the following (i) 52 moles of Ar (ii) 52 u of He (iii) 52 g of He
(i) 52 moles of Ar 1 mole of Ar = $6.023 \; \times \; 10^{ 23 }$atoms of Ar Therefore, 52 mol of Ar = 52 × $6.023 \; \times \; 10^{ 23 }$atoms of Ar = $3.131 \; \times \; 10^{ 25 }$ atoms of Ar...
A welding fuel gas contains carbon and hydrogen only. Burning a small sample of it in oxygen gives 3.38 g carbon dioxide, 0.690 g of water and no other products. A volume of 10.0 L (measured at STP) of this welding gas is found to weigh 11.6 g. Find: (i) Empirical formula (ii) Molar mass of the gas, and (iii) Molecular formula
(i) Empirical formula 1 mole of $CO_{ 2 }$ contains 12 g of carbon Therefore, 3.38 g of $CO_{ 2 }$ will contain carbon = $\frac{ 12 \; g }{ 44 \; g } \; \times 3.38 \; g$ = 0.9217 g 18 g of...
Calcium carbonate reacts with aqueous HCl to give CaCl2 and CO2 according to the reaction, CaCO3 (s) + 2 HCl (aq) → CaCl2(aq) + CO2 (g) + H2O(l) What mass of CaCO3 is required to react completely with 25 mL of 0.75 M HCl?
0.75 M of HCl ≡ 0.75 mol of HCl are present in 1 L of water ≡ $[(0.75 mol)\times(36.5 g mol–1 )]$ HCl is present in 1 L of water ≡ 27.375 g of HCl is present in 1 L of water Thus, 1000 mL of...
Chlorine is prepared in the laboratory by treating manganese dioxide (MnO2) with aqueous hydrochloric acid according to the reaction: 4 HCl (aq) + MnO2(s) → 2H2O (l) + MnCl2(aq) + Cl2 (g) How many grams of HCl react with 5.0 g of manganese dioxide?
1 mol of $MnO_{2}$ = 55 + 2 × 16 = 87 g 4 mol of HCl = 4 × 36.5 = 146 g 1 mol of $MnO_{2}$ reacts with 4 mol of HCl 5 g of $MnO_{ 2 }$will react with: =$ \frac{146 \; g}{87 \; g} \; \times \; 5...
In a reaction A + B2 → AB2 Identify the limiting reagent, if any, in the following reaction mixtures. (i) 300 atoms of A + 200 molecules of B (ii) 2 mol A + 3 mol B (iii) 100 atoms of A + 100 molecules of B (iv) 5 mol A + 2.5 mol B (v) 2.5 mol A + 5 mol B
Reagent limitation: It establishes the magnitude of a reaction. It is the first to be consumed in a reaction, causing the process to come to a halt and limiting the number of products produced. (i)...
If the speed of light is 3.0 × 10^8 m s^(–1), calculate the distance covered by light in 2.00 ns
Time taken = 2 ns = $2 \times10^{ -9 }$ s Now, Speed of light =$3 \times10^{ 8 } ms^{ -1 }$ So, Distance travelled in 2 ns = speed of light * time taken =$(3 \times10^{ 8 })(2 \times10^{ -9 })$ = $6...
The following data are obtained when dinitrogen and dioxygen react together to form different compounds:;(a) Which law of chemical combination is obeyed by the above experimental data? Give its statement. (b) Fill in the blanks in the following conversions: (i) 1 km = …………………. mm = …………………. pm (ii) 1 mg = …………………. kg = …………………. ng (iii) 1 mL = …………………. L = …………………. dm3
(a) If the mass of N2 is set at 28 g, the mass of O2 that will combine with it is 32 grammes, 64 grammes, 32 grammes, and 80 grammes. O2 has a mass-to-number ratio of 1: 2: 1: 5. As a result, the...
Round up the following upto three significant figures: (a) 34.216 (b) 10.4107 (c)0.04597 (d)2808
(a) The number after round up is: 34.2 (b) The number after round up is: 10.4 (c)The number after round up is: 0.0460 (d)The number after round up is: 2808
How many significant figures are present in the following? (a) 0.0027 (b) 209 (c) 6005 (d) 136,000 (e) 900.0 (f) 2.0035
(i) 0.0027: 2 significant numbers. (ii) 209: 3 significant numbers. (iii) 6005: 4 significant numbers. (iv) 136,000:3 significant numbers. (v) 900.0: 4 significant numbers. (vi) 2.0035: 5...
Express the following in the scientific notation: (i) 0.0048 (ii) 234,000 (iii) 8008 (iv) 500.0 (v) 6.0012
(a$) 0.0048= 4.8 \times10^{-3}$ (b) $234,000 = 2.34 \times10^{5}$ (c) $8008= 8.008 \times10^{3}$ (d) $500.0 = 5.000 \times10^{2}$ (e) $6.0012 = 6.0012 \times10^{0}$
A sample of drinking water was found to be severely contaminated with chloroform, CHCl3, supposed to be carcinogenic in nature. The level of contamination was 15 ppm (by mass). (i) Express this in per cent by mass. (ii) Determine the molality of chloroform in the water sample.
(a) $1 ppm = 1 part out of 1 million parts.$ Mass percent of 15 ppm chloroform in H2O= $\frac{15}{{{10}^{6}}}\times 100$ $\approx 1.5 \times{10}^{-3}%$ $ (b)$100 grams of the sample is having 1.5 ×...
What do you mean by significant figures?
The meaningful numbers that are known with certainty are known as significant figures. Significant numbers imply that the tested value is unknown. For example, if the experiment yielded 15.6 mL, 15...
Match the following prefixes with their multiples:
What is the SI unit of mass? How is it defined?
Kilogram is the SI unit of mass (kg) Mass: “Mass is defined as the mass equivalent to the mass of the international kilogramme prototype.”
Pressure is determined as force per unit area of the surface. The SI unit of pressure, pascal is as shown below: 1Pa = 1N m–2 If mass of air at sea level is 1034 g cm–2, calculate the pressure in pascal
As per definition, pressure is force per unit area of the surface. $P = \frac{F}{A}$ =$ \frac{1034\;g\;\times \;9.8\;ms^{-2}}{cm^{2}}\times \frac{1\;kg}{1000\;g}\times \frac{(100)^{2}\;cm^{2}}{1...
If the density of methanol is 0.793 kg 
, what is its volume needed for making 2.5 L of its 0.25 M solution?
$Molar mass of CH_{3}OH$ = (1 * 12) + (4 * 1) + (1 * 16) =$32 g mol^{-1}$ = $0.032 kg mol^{-1}$ Molarity of the solution = $\frac{0.793\;kg\;L^{-1}}{0.032\;kg\;mol^{-1} }$ = 24.78 mol{L}^{-1}...
What is the concentration of sugar
in mol 
if its 20 g are dissolved in enough water to make a final volume up to 2L?
Molarity (M) is as given by, = $\frac{Number\;of\;moles\;of\;solute}{Volume\;of\;solution\;in\;Litres}$ =$\frac{\frac{Mass\;of\;sugar}{Molar\;mass\;of\;sugar}}{2\;L}$ =...
A person driving a car suddenly applies the brakes on seeing a child on the road ahead. If he is not wearing a seat belt, he falls forward and hits his head against the steering wheel. Why?
If a person is not wearing a seat belt and abruptly hits the brakes, he will fall forward and bang his head against the steering wheel because his upper body will continue to move in the same...
The position time graph of a body of mass 2 kg is as given in the figure. What is the impulse on the body at t – 0 sec and t = 4 sec.
Mass of body, m = 2 kg Time, t = 0 Initial velocity, v1 = 0 From graph, we know that t ≥ 0 to t ≤ 4 which is a straight line. The velocity of the body is constant v2 = tan θ = 3/4 = 0.75 m/s At t ≥...
A person of mass 50 kg stands on a weighing scale on a lift. If the lift is descending with a downward acceleration of 9 m/s2 what would be the reading of the weighing scale?
When the lift lowers with an acceleration a, the apparent weight on the weighing scale decreases. W' denotes the apparent weight. Therefore, W' = R = (mg – ma) = m(g – a) As a result, W' = 50(10-9)...
A girl riding a bicycle along a straight road with a speed of 5 m/s throws a stone of mass 0.5 kg which has a speed of 15 m/s with respect to the ground along her direction of motion. The mass of the girl and the bicycle is 50 kg. Does the speed of the bicycle change after the stone is thrown? What is the change in speed, if so?
Given, m1 = 50 kg m2 = 0.5 kg u1 = 5 m/s u2 = 5 m/s v1 = ? v2 = 15 m/s The law of conservation of momentum states that Final momentum equals initial momentum. u1 = m1v1 + m2v2 (m1 + m2) We obtain by...
A body of mass 10 kg is acted upon by two perpendicular forces, 6N and 8N. The resultant acceleration of the body is a) 1 m/s2 at an angle of tan-1 (4/3) w.r.t 6N force b) 0.2 m/s2 at an angle of tan-1 (4/3) w.r.t 6N force c) 1 m/s2 at an angle of tan-1(3/4) w.r.t 8N force d) 0.2 m/s2 at an angle of tan-1(3/4) w.r.t 8N force
The correct answers are a) 1 m/s2 at an angle of tan-1 (4/3) w.r.t 6N force c) 1 m/s2 at an angle of tan-1(3/4) w.r.t 8N force
Two billiard balls A and B, each of mass 50 g and moving in opposite directions with speed of 5 m/s each, collide and rebound with the same speed. If the collision lasts for 10-3 seconds, which of the following statements are true? a) the impulse imparted to each ball is 0.25 kg.m/s and the force on each ball is 250N b) the impulse imparted to each ball is 0.25 kg.m/s and the force exerted on each ball is 25 × 10-5 N c) the impulse imparted to each ball is 0.5 Ns d) the impulse and the force on each ball are equal in magnitude and opposite in direction
The correct answer is: c) the impulse imparted to each ball is 0.5 Ns d) the impulse and the force on each ball are equal in magnitude and opposite in direction
In the figure, a body A of mass m slides on a plane inclined at angle θ1 to the horizontal and μ1 is the coefficient of friction between A and the plane. A is connected by a light string passing over a frictionless pulley to another body B, also of mass m, sliding on a frictionless plane inclined at angle θ2 to the horizontal. Which of the following statements are true?;a) A will never move up the plane b) A will just start moving up the plane when 
c) for A to move up the plane, θ2 must always be greater than θ1 d) B will always slide down with constant speed
The correct answer is: b) A will just start moving up the plane when \(\mu =\frac{\sin {{\theta }_{2}}-\sin {{\theta }_{1}}}{\cos {{\theta }_{1}}}\) c) for A to move up the plane, θ2 must always be...
Mass m1 moves on a slope making an angle θ with the horizontal and is attached to mass m2 by a string passing over a frictionless pulley as shown in the figure. The coefficient of friction between m1 and the sloping surface is μ. Which of the following statements are true?;a) if m2 > m1 sin θ, the body will move up the plane b) if m2 > m1(sin θ + μ cos θ), the body will move up the plane c) if m2 < m1 (sin θ + μ cos θ), the body will move up the plane d) if m2 < m1 (sin θ – μ cos θ), the body will move down the plane
The correct answer is: b) if m2 > m1(sin θ + μ cos θ), the body will move up the plane d) if m2 < m1 (sin θ – μ cos θ), the body will move down the plane
In figure, the coefficient of friction between the floor and the body B is 0.1. The coefficient of friction between the bodies B and A is 0.2. A force F is applied as shown on B. The mass of A is m/2 and of B is m. Which of the following statements are true?;a) the bodies will move together if F = 0.25 mg b) the body A will slip with respect to B if F = 0.5 mg c) the bodies will move together if F = 0.5 mg d) the bodies will be at rest if F = 0.1 mg e) the maximum value of F for which the two bodies will move together is 0.45 mg
The correct answer is: a) the bodies will move together if F = 0.25 mg b) the body A will slip with respect to B if F = 0.5 mg d) the bodies will be at rest if F = 0.1 mg e) the maximum value of F...
The motion of a particle of mass m is given by x = 0 for t < 0 sec, x(t) = A sin 4p t for 0 < t < (1/4) sec, and x = 0 for t > (1/4) sec. Which of the following statements is true? a) the force at t = (1/8) sec on the particle is -16π2Am b) the particle is acted upon by on impulse of magnitude 4π2Am at t = 0 sec and t = (1/4) sec c) the particle is not acted upon by any force d) the particle is not acted upon by a constant force e) there is no impulse acting on the particle
The correct answer is: a) the force at t = (1/8) sec on the particle is -16π2Am b) the particle is acted upon by on impulse of magnitude 4π2Am at t = 0 sec and t = (1/4) sec d) the particle is not...
A car of mass m starts from rest and acquires a velocity along the east a in two seconds. Assuming the car moves with uniform acceleration, the force exerted on the car is a) mv/2 eastward and is exerted by the car engine b) mv/2 eastward and is due to the friction on the tyres exerted by the road c) more than mv/2 eastward exerted due to the engine and overcomes the friction of the road d) mv/2 exerted by the engine
The correct answer is b) mv/2 eastward and is due to the friction on the tyres exerted by the road
A body with mass 5 kg is acted upon by a force F=-3i+4j N. If its initial velocity at t = 0 is v=6i-12j m/s, the time at which it will just have a velocity along the y-axis is a) never b) 10 s c) 2 s d) 15 s
The correct answer is b) 10 s
A body of mass 2 kg travels according to the law x(t) = p(t) + qt2 + rt3 where p = 3 m/s, q = 4 m/s2, and r = 5 m/s3. The force acting on the body at t=2 seconds is a) 136 N b) 134 N c) 158 N d) 68 N
The correct answer is a) 136 N
A hockey player is moving northward and suddenly turns westward with the same speed to avoid an opponent. The force that acts on the player is a) frictional force along westward b) muscle force along southward c) frictional force along south-west d) muscle force along south-west
The correct answer is c) frictional force along the south-west
Conservation of momentum in a collision between particles can be understood from a) conservation of energy b) Newton’s first law only c) Newton’s second law only d) both Newton’s second and third law
The correct answer is d) both Newton’s second and third law
In the previous problem, the magnitude of the momentum transferred during the hit is a) zero b) 0.75 kg.m/s c) 1.5 kg.m/s d) 14 kg.m/s
The correct option is c) 1.5 kg.m/s
A cricket ball of mass 150 g has an initial velocity u=3i+4j m/s and a final velocity v=-(3i+4j) m/s after being hit. The change in momentum a) zero (b)-(0.45i+0.6j) (c)-(0.9i+1.2j)) (d)-5(i+j)
The correct answer is (c) -(0.9i+1.2j)
A metre scale is moving with uniform velocity. This implied a) the force acting on the scale is zero, but a torque about the centre of mass can act on the scale b) the force acting on the scale is zero and the torque acting about the centre of mass of the scale is also zero c) the total force acting on it need not be zero but the torque on it is zero d) neither the force nor the torque needs to be zero
The correct answer is b) the force acting on the scale is zero and the torque acting about the centre of mass of the scale is also zero
A ball is travelling with uniform translator motion. This means that a) it is at rest b) the path can be a straight line or circular and the ball travels with uniform speed c) all parts of the ball have the same velocity and the velocity is constant d) the centre of the ball moves with constant velocity and the ball spins about its centre uniformly
The correct option is c) all parts of the ball have the same velocity and the velocity is constant
A balloon filled with helium rises against gravity increasing its potential energy. The speed of the balloon also increases as it rises. How do you reconcile this with the law of conservation of mechanical energy? You can neglect the viscous drag of air and assume that the density of air is constant.
The net buoyant force Equals vpg when the dragging viscous force of the air on the balloon is ignored. Where v is the volume of air that has been displaced. The upward net density is denoted by p....
Two identical steel cubes collide head-on face to face with a speed of 10 cm/s each. Find the maximum compression of each. Young’s modulus for steel = Y = 2 × 1011 N/m2.
Y = stress/strain Y = FL/A∆L WD = F∆L KE = 5 × 10-4 J WD = KE ∆L = 5 × 10-7 m
A rocket accelerates straight up by ejecting gas downwards. In a small time interval ∆t, it ejects a gas of mass ∆m at a relative speed u. Calculate KE of the entire system at t + ∆t and t and show that the device that ejects gas does work = (1/2) ∆m u2 in this time interval.
M is the rocket's mass at any given moment t. The rocket's velocity is v. The mass of the gas expelled during the time interval t is m. As a result, K = 1/2 u2∆m
A curved surface as shown in the figure. The portion BCD is free of friction. There are three spherical balls of identical radii and masses. Balls are released from one by one from A which is at a slightly greater height than C. with the surface AB, ball 1 has large enough friction to cause rolling down without slipping; ball 2 has a small friction and ball 3 has a negligible friction. a) for which balls is total mechanical energy conserved? b) which ball can reach D? c) for balls which do not reach D, which of the balls can reach back A?
a) For ball 1 the total mechanical energy is conserved b) Ball 1 reaches D c) Ball 3 reaches back A
A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of 30o by a force of 10 N parallel to the inclined surface. The coefficient of friction between the block and the incline is 0.1. If the block is pushed up by 10 m along the incline, calculate a) work done against gravity b) work done against the force of friction c) increase in potential energy d) increase in kinetic energy e) work done by an applied force
a) Work against gravity equals mgh 5 m= h 50 J WD against gravity b) The work done against the friction force is fs = 53 J. d) WD against gravity = 50 J increase in PE d) The system's increase in KE...
On complete combustion, a litre of petrol gives off heat equivalent to 3 × 107 J. In a test drive a car weighing 1200 kg, including the mass of driver, runs 15 km per litre while moving with a uniform speed on a surface and air to be uniform, calculate the force of friction acting on the car during the test drive, if the efficiency of the car engine were 0.5.
car engine Efficiency = 0.5 Energy given by the car with 1 litre of petrol = 1.5 × 107 WD = 1.5 × 107 f = 103 N
An adult weighing 600 N raises the centre of gravity of his body by 0.25 m while taking each step of 1 m length in jogging. If he jogs for 6 km, calculate the energy utilized by him in jogging assuming that there is no energy loss due to friction of ground and air. Assuming that the body of the adult is capable of converting 10% of energy intake in the form of food, calculate the energy equivalents of food that would be required to compensate energy utilized for jogging.
The energy used up is given as = mgh mg = 600 N h = 0.25m No.of steps in 6 km = 6000 steps Energy used in 6000 m = (6000)(600)(0.25)J Energy utilized in jogging = 9 × 104 J
An engine is attached to a wagon through a shock absorber of length 1.5 m. The system with a total mass of 50,000 kg is moving with a speed of 36 km/h when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by 1.0 m. If 90% of the energy of the wagon is lost due to friction, calculate the spring constant.
KE = 1/2 mv2 m = 50000 kg v = 10 m/s KE = 2500000J KE of spring = 10% of the KE wagon K = 5 × 105 N/m
Suppose the average mass of raindrops is 3.0 × 10^(-5) kg and their average terminal velocity 9 m/s. Calculate the energy transferred by rain to each square meter of the surface at a place which receives 100 cm of rain in a year.
Energy transferred by the rain to the surface of the earth = 1/2 mv2 The velocity of the rain = 9 m/s Mass = (volume)(density) = 1000 kg Energy transferred by 100 cm rainfall = 1/2 mv2 =...
Two pendulums with identical bobs and lengths are suspended from a common support such that in rest position the two bobs are in common. One of the bobs is released after being displaced by 10o so that it collides elastically head-on with the other bob. a) describe the motion of two bobs b) draw a graph showing variation in energy of either pendulum with time for 0 ≤ t ≤ 2T where T is the period of each pendulum
A raindrop of mass 1.00 g falling from a height of 1 km hits the ground with a speed of 50 m/s. Calculate a) the loss of PE of the drop b) the gain in KE of the drop c) is the gain in KE equal to loss of PE? If not why?
a) PE at the highest point = 10 J b) Gain in KE = 1/2 mv2 = 1.250 J c) Gain in KE is not equal to the PE
The bob A of a pendulum released from horizontal to the vertical hits another bob B of the same mass at rest on a table as shown in the figure. If the length of the pendulum is 1 m, calculate a) the height to which bob A will rise after collision b) the speed with which bob B starts moving. Neglect the size of the bobs and assume the collision to be elastic.
a) After the impact, bob A does not rise much because the PE of bob A is converted to KE and the momentum is transferred to bob B. (B) The speed of bob B is calculated as the sum of bob A's KE and...
Consider a one-dimensional motion of a particle with total energy E. There are four regions A, B, C, and D in which the relation between potential energy V, kinetic energy (K) and total energy is as given below: Region A: V > E Region B: V < E Region C: K > E Region D: V > K State with reason in each case whether a particle can be found in the given region or not.
E = V + K and V > E for area A, implying that the KE is negative and therefore this is not feasible. K = E – V and V E for area B, implying that both energies are larger than zero. V = E – K and...
A ball of mass m, moving with a speed 2v0 collides inelastically with an identical ball at rest. Show that a) for a head-on collision, both the balls move forward b) for a general collision, the angle between the two velocities of scattered balls is less than 90o.
a) Let v1 and v2 be the velocities of the two balls after the collision. According to the law of conservation of momentum, mv0 = mv1 + mv2 v2 = v1 + 2ev0 e < 1 b) Using the law of conservation of...
A graph of potential energy V(x) versus x is shown in the figure. A particle of energy E0 is executing motion in it. Draw graph of velocity and kinetic energy versus x for one complete cycle AFA.
From the given graph of KE versus x From the below graph of velocity versus x
A bob of mass m suspended by a light string of length L is whirled into a vertical circle as shown in the figure. What will be the trajectory of the particle if the string is cut at a) point B b) point C c) point X
a) When the string is severed at point B, the particle's tangential velocity will be vertically downward, and the bob will travel in the same direction. b) When the string is severed at point C, the...
Two bodies of unequal mass are moving in the same direction with equal kinetic energy. The two bodies are brought to rest by applying retarding force of the same magnitude. How would the distance moved by them before coming to rest compare?
KE1 = KE2 WD1 = WD2 F1s1 = F2s2 F1 = F2 s1 = s2
Give an example of a situation in which an applied force does not result in a change in kinetic energy.
The kinetic energy of work done in a circular motion remains unchanged.
The average work done by a human heart while it beats once is 0.5 J. Calculate the power used by heart if it beats 72 times in a minute.
P = WD/time WD is one beat of heart = 0.5 J WD in 72 beats = 36 J P = WD/t = 0.6 W
Calculate the power of a crane in watts, which lifts a mass of 100 kg to a height of 10 min 20 sec.
P = WD/time = Fs cos θ/t = mgh cos θ/t h = 10 m t = 20 sec F = mg = 1000 Therefore, P = 500 Watts
In an elastic collision of two billiard balls, which of the following quantities remain conserved during the short time of collision of the balls a) kinetic energy b) total linear momentum Give a reason for your answer in each case.
Because there is no non-conservative force, the kinetic energy and total linear momentum of the billiard balls are preserved.
A body is moved along a closed loop. Is the work done in moving the body necessarily zero? If not, state the condition under which work done over a closed path is always zero.
When the conservative force acts on the body during motion, the work done by the moving body is zero. When a non-conservative force acts on a moving body, the work done by the body is not zero.
A body falls towards earth in the air. Will its total mechanical energy be conserved during the fall? Justify.
The free-falling body's total mechanical energy is not preserved since it is utilised to overcome the frictional force of the air molecules.
Calculate the work done by a car against gravity in moving along a straight horizontal road. The mass of the car is 400 kg and the distance moved is 2m.
WD = Fs cos θ WD = Fs cos 90o = 0 Hence, the work done by the car against the gravity is zero.
A body is being raised to a height h from the surface of the earth. What is the sign of work done by a) applied force b) gravitational force
a) The applied force produces positive work. b) The gravitational pull produces negative work.
Why is electrical power required at all when the elevator is descending? Why should there be a limit on the number of passengers in this case?
In the event of an elevator falling, the number of passengers is limited because it is not a free fall and descends at a constant speed.
A rough inclined plane is placed on a cart moving with a constant velocity u on horizontal ground. A block of mass M rests on the incline. Is any work done by a force of friction between the block and incline? Is there then a dissipation of energy?
The block is clearly tilted on the plane in the illustration above. There is no work done since there is no displacement and no waste of energy.
Two blocks M1 and M2 having equal mass are free to move on a horizontal frictionless surface. M2 is attached to a massless spring as shown in the figure. Initially, M2 is at rest and M1 is moving toward M2 with speed v and collides head-on with M2.;a) while spring is fully compressed all the KE of M1 is stored as PE of spring b) while spring is fully compressed the system momentum is not conserved, though final momentum is equal to the initial momentum c) if spring is massless, the final state of the M1 is the state of rest d) if the surface on which blocks are moving has friction, then a collision cannot be elastic
c) if spring is massless, the final state of the M1 is a state of rest d) if the surface on which blocks are moving has friction, then a collision cannot be elastic
A bullet of mass m fired at 30o to the horizontal leaves the barrel of the gun with a velocity v. The bullet hits a soft target at a height h above the ground while it is moving downward and emerges out with half the kinetic energy it had before hitting the target. Which of the following statements are correct in respect of bullet after it emerges out of the target? a) the velocity of the bullet will be reduced to half its initial value b) the velocity of the bullet will be more than half of its earlier velocity c) the bullet will continue to move along the same parabolic path d) the bullet will move in a different parabolic path e) the bullet will fall vertically downward after hitting the target f) the internal energy of the particles of the target will increase
b) the velocity of the bullet will be more than half of its earlier velocity d) the bullet will move in a different parabolic path f) the internal energy of the particles of the target will...
A man, of mass m, standing at the bottom of the staircase, of height L, climbs it and stands at its top. a) work done by all forces on man is zero b) work done by all the force on man is zero c) work done by the gravitational force on man is mgL d) the reaction force from a step does not do work because the point of application of the force does not move while the force exists
b) work done by all the force on man is zero d) the reaction force from a step does not do work because the point of application of the force does not move while the force exists
A cricket ball of mass 150 g moving with a speed of 126 km/h hits at the middle of the bat, held firmly at its position by the batsman. The ball moves straight back to the bowler after hitting the bat. Assuming that collision between ball and bat is completely elastic and the two remain in contact for 0.001 sec, the force that the batsman had to apply to hold the bat firmly at its place would be a) 10.5 N b) 21 N c) 1.05 × 
N d) 
N
c) 1.05 × 104 N
Which of the diagrams in figure correctly shows the change in kinetic energy of an iron sphere falling freely in a lake having sufficient depth to impart it a terminal velocity?
(b
In a shotput event an athlete throws the shotput of mass 10 kg with an initial speed of 1 m/s at 45o from height 1.5 m above ground. Assuming air resistance to be negligible and acceleration due to gravity to be 10 m/s2, the kinetic energy of the shotput when it just reaches the ground will be a) 2.5 J b) 5.0 J c) 52.5 J d) 155.0 J
d) 155.0 J
A raindrop falling from a height h above ground, attains a near-terminal velocity when it has fallen through a height (3/4)h. Which of the diagrams show correctly the change in kinetic and potential energy of the drop during its falls up to the ground?
b)
A mass of 5 kg is moving along a circular path of radius 1 m. If the mass moves with 300 revolutions per minute, its kinetic energy would be a) 250π2 b) 100 π2 c) 5 π2 d) 0
a) 250π2
Which of the diagrams shown in the figure represents variations of total mechanical energy of a pendulum oscillating in air as a function of time?
c)
Which of the diagrams shown in figure most closely shows the variation in kinetic energy of the earth as it moves once around the sun in its elliptical orbit?
d)
A body is moving unidirectionally under the influence of a source of constant power supplying energy. Which of the diagrams shown in the figure correctly shows the displacement-time curve for its motion?
b)
A body of mass 0.5 kg travels in a straight line with velocity v = ax3/2 where a = 5 m-1/2s-1. The work done by the net force during its displacement from x = 0 to x = 2 m is a) 1.5 J b) 50 J c) 10 J d) 100 J
b) 50 J
Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed V as shown:If the collision is elastic, which of the following is a possible result after collision?
\b)
The potential energy function for a particle executing linear SHM is given by where k is the force constant of the oscillator. For k = 0.5 N/m, the graph of V(x) versus x is shown in the figure. A particle of total energy E turns back when it reaches x = ±xm, then which of the following is correct?a) V = O, K = E b) V = E, K = O c) V < E, K = O d) V = O, K < E
b) V = E, K = O
Two inclined frictionless tracks, one gradual and the other steep meet at A from where two stones are allowed to slide down from rest, one on each track as shown in the figure. Which of the following statement is correct?a) both the stones reach the bottom at the same time but not with the same speed b) both stone reach the bottom with the same speed and stone I reaches the bottom earlier than stone II c) both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone I d) both the stones reach the bottom at different times and with different speeds
c) both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone I
During inelastic collision between two bodies, which of the following quantities always remain conserved? a) total kinetic energy b) total mechanical energy c) total linear momentum d) speed of each body
c) total linear momentum
A body is falling freely under the action of gravity alone in a vacuum. Which of the following quantities remain constant during the fall? a) kinetic energy b) potential energy c) total mechanical energy d) total linear momentum
c) total mechanical energy
A bicyclist comes to a skidding stop in 10 m. During this process, the force on the bicyclist due to the road is 200 N and is directly opposed to the motion. The work done by the cycle on the road is a) +2000 J b) -200 J c) zero d) -20,000 J
c) zero
A man squatting on the ground gets straight up and stand. The force of reaction of ground on the man during the process is a) constant and equal to mg in magnitude b) constant and greater than mg in magnitude c) variable but always greater than mg d) at first greater than mg, and later becomes equal to mg
d) at first greater than mg, and later becomes equal to mg
A proton is kept at rest. A positively charged particle is released from rest at a distance d in its field. Consider two experiments; one in which the charged particles is also a proton and in another, a positron. In the same time t, the work done on the two moving charged particles is a) the same as the same force law is involved in the two experiments b) less for the case of a positron, as the positron moves away more rapidly and the force on it weakens c) more for the case of a positron, as the positron moves away from a larger distance d) same as the work done by charged particle on the stationary proton
c) more for the case of a positron, as the positron moves away from a larger distance
An electron and a proton are moving under the influence of mutual forces. In calculating the change in the kinetic energy of the system during motion, one ignores the magnetic force of one on another. This is because, a) the two magnetic forces are equal and opposite, so they produce no net effect b) the magnetic forces do no work on each particle c) the magnetic forces do equal and opposite work on each particle d) the magnetic forces are necessarily negligible
b) the magnetic forces do no work on each particle
Five long wires A, B, C, D, and E each carrying I are arranged to form edges of a pentagonal prism as shown in the figure. Each carries current out of the plane of paper. a) what will be magnetic induction at a point on the axis O> Axis is at a distance R from each wire b) what will be the field if current in one of the wires is switched off c) what if current in one of the wire A is reversed
(a) Because A, B, C, D, and E are perpendicular to the plane of paper at the specified places, the magnetic induction at a point on the axis will be zero, which is represented by R. (b) The field...
A multirange current meter can be constructed by using a galvanometer circuit shown in the figure. We want a current meter that can measure 10 mA, 100 mA, and 1 A using a galvanometer of resistance 10Ω and that produces maximum deflection for a current of 1 mA. Find S1, S2, and S3 that have to be used.
I1 is measured as = 10 mA = IGG = (I1 – IG)(S1 + S2 + S3) I2 is measured as = 100 mA = IG(G+S1)=(I2-IG)(S2-S3) I3 is measured as = 1 A = IG(G+S1+S2)=(I3-IG)(S3) S1 = 1 Ω S2 = 0.1 Ω S3 = 0.01...
Consider a circular current-carrying loop of radius R in the x-y plane with centre at the origin. Consider the line integral
a) show that
monotonically increases with L b) use an appropriate Amperian loop to that
where I is the current in the wire c) verify directly the above result d) suppose we replace the circular coil by a square coil of sides R carrying the same current I. What can you say about
a) A circular current-carrying loop's magnetic field is given as \(\Im (L)=\int_{-L}^{+L}{Bdl}=2Bl\) It is a L function that increases monotonically. b) The Amperian loop is defined as follows:...
A uniform conducting wire of length 12a and resistance R is wound up as a current-carrying coil in the shape of i) an equilateral triangle of side a; ii) a square if sides a and iii) a regular hexagon of sides a. The coil is connected to a voltage source V0. Find the magnetic moment of the coils in each case.
a) A triangle with side a that is equilateral. Number of loops = 4 A = √3/4 a2 m = Ia2√3 is the magnetic moment. b) In the case of a square with sides of a A = a2 Number of loops = 3 m =...
An electron and a positron are released from (0, 0, 0) and (0, 0, 1.5R) respectively, in a uniform magnetic field each with an equal momentum of magnitude p = eBR. Under what conditions on the direction of momentum will the orbits be non-intersecting circles?
The circular orbits of electron and positron should not overlap when the centres are bigger than 2R. Let the distance between Cp and Ce be denoted by d. Then d2 = 4R2 + 9/4R2 – 6R2 cosθ Because d...
A rectangular conducting loop consists of two wires on two opposite sides of length l joined together by rods of length d. The wires are each of the same material but with cross-sections differing by a factor of 2. The thicker wire has a resistance R and the rods are of low resistance, which in turn are connected to a constant voltage source Vo. The loop is placed in uniform a magnetic field B at 45oto its plane. Find τ, the torque exerted by the magnetic field on the loop about an axis through the centres of rods.
F1 = i1l B sin 90o = V0/2R lB τ1= d/2√2 F1 = V0ldB/2√2 R τ = 1/4√2 V0AB/R
A 100 turn rectangular coil ABCD is hung from one arm of a balance. A mass 500 g is added to the other arm to balance the weight of the coil. A current 4.9 A passes through the coil and a constant magnetic field of 0.2 T acting inward is switched on such that only arm CD of length 1 cm lies in the field. How much additional mass ‘m’ must be added to regain the balance?
When t = 0, the external magnetic field is off. Mgl = Wcoil l 0.5 gl = Wcoil l Wcoil = 0.5 9.8 N Let m be the mass that is added to restore equilibrium. The magnetic field is activated when the...
A long straight wire carrying a current of 25 A rests on a table as shown in the figure. Another wire PQ of length 1 m, mass 2.5 g carries the same current but in the opposite direction. The wire PQ is free to slide up and down. To what height will PQ rise?
The magnetic field produced by a long straight current-carrying wire is given as B = μ0I/2πh Magnetic force on the small conductor is F = BIl sin θ = BIl F = mg = μ0I2l/2πh h = 0.51...
A multirange voltmeter can be constructed by using a galvanometer circuit as shown in the figure. We want to construct a voltmeter that can measure 2V, 20V, and 200V using galvanometer of resistance 10Ω and that produces maximum deflection for a current of 1 mA. Find R1, R2, and R3 that have to be used.
iG(G+R1) = 2 for 2V range iG(G+R1+R2) = 20 for 20V range iG(G+R1+R2+R3) = 200 for 200V range Solving the above, we get R1 = 1990 Ω R2 = 18kΩ R3 = 180 kΩ
Do magnetic forces obey Newton’s third law. Verify for two current elements located at the origin and located at (0,R,0). Both carry current I.
If there is no current flowing in the conductors that are parallel to each other, the magnetic forces do not obey Newton's third law.
An electron enters with a velocity v = v0i into a cubical region in which there are uniform electric and magnetic fields. The orbit of the electron is found to spiral down inside the cube in the plane parallel to the x-y plane. Suggest a configuration of fields E and B that can lead to it.
The spiral route is formed by the fields E and B in their current configuration.
A charged particle of charge e and mass m is moving in an electric field E and magnetic field B. Construct dimensionless quantities and quantities of dimension [T]-1.
mv2/R = evB eB/m = v/R = ꞷ B = F/ev = [MA-1T-2] [ꞷ] = [eB/m]=[v/R] = [T-1]
A current-carrying loop consists of 3 identical quarter circles of radius R, lying in the positive quadrants of the x-y, y-z, and z-x planes with their centres at the origin, joined together. Find the direction and magnitude of B at the origin.
The quarter's vector sum of the magnetic field at the origin is given as \({{\vec{B}}_{net}}=\frac{1}{4}\left( \frac{{{\mu }_{0}}I}{2R} \right)(\widehat{i}+\widehat{j}+\widehat{k})\)
Describe the motion of a charged particle in a cyclotron if the frequency of the radio frequency (rf) field were doubled.
The time period of the radio frequency is halved when the frequency is doubled, resulting in a half revolution of the charges.
The magnetic force depends on v which depends on the inertial frame of reference. Does then the magnetic force differ from inertial frame to frame? Is it reasonable that the net acceleration has a different value in different frames of reference?
Because velocity varies depending on frame of reference, the net acceleration might have a different value in different frames of reference.
Show that a force that does no work must be a velocity dependent force.
\(dW=\vec{F}\cdot dl=0\) \(\vec{F}\cdot \vec{v}=0\)
Verify that the cyclotron frequency ꞷ = eB/m has the correct dimensions of [T]-1.
In a cyclotron, the particle follows a circular path, with magnetic force acting as a centripetal force. mv2/R = evB eB/m = v/R = ꞷ B = F/ev = [MLT-2]/[AT][LT-1] = [MA-1T-2] [ꞷ] = [eB/m] = [v/R] =...
A charged particle would continue to move with a constant velocity in a region wherein, a) E = 0, B ≠ 0 b) E ≠ 0, B ≠ 0 c) E ≠ 0, B = 0 d) E = 0, B = 0
a) E = 0, B ≠ 0 b) E ≠ 0, B ≠ 0 d) E = 0, B = 0
A cubical region of space is filled with some uniform electric and magnetic fields. An electron enters the cube across one of its faces with velocity v and a positron enters via opposite face with velocity –v. At this instant, a) the electric forces on both the particles cause identical acceleration b) the magnetic forces on both the particles cause equal accelerations c) both particles gain or lose energy at the same rate d) the motion of the centre of mass (CM) is determined by B alone
b) the magnetic forces on both the particles cause equal accelerations c) both particles gain or lose energy at the same rate d) the motion of the centre of mass (CM) is determined by B alone
Two identical current-carrying coaxial loops, carry current I in an opposite sense. A simple amperian loop passes through both of them once. Calling the loop as C, a)
b) the value of
c) there may be a point on C where B and dl are perpendicular d) B vanishes everywhere on C
b) the value of \(\oint\limits_{c}{B.dl\) is independent of sense of C c) there may be a point on C where B and dl are perpendicular
Consider a wire carrying a steady current, I placed un a uniform magnetic field B perpendicular to its length. Consider the charges inside the wire. It is known that magnetic forces do not work. This implies that a) motion of charges inside the conductor is unaffected by B since they do not absorb energy b) some charges inside the wire move to the surface as a result of B c) if the wire moves under the influence of B, no work is done by the force d) if the wire moves under the influence of B, no work is done by the magnetic force on the ions, assumed fixed within the wire
b) some charges inside the wire move to the surface as a result of B d) if the wire moves under the influence of B, no work is done by the magnetic force on the ions, assumed fixed within the wire
The gyro-magnetic ratio of an electron in an H-atom, according to Bohr model is a) independent of which orbit it is in b) negative c) positive d) increases with the quantum number n
a) independent of which orbit it is in b) negative
A circular current loop of magnetic moment M is in an arbitrary orientation in an external magnetic field B. The work done to rotate the loop by 30o about an axis perpendicular to its plane is a) MB b) √3 MB/2 c) MB/2 d) zero
d) zero
In a cyclotron, a charged particle a) undergoes acceleration all the time b) speeds up between the dees because of the magnetic field c) speeds up in a dee d) slows down within a dee and speeds up between dees
a) undergoes acceleration all the time
An electron is projected with uniform velocity along the axis of a current-carrying long solenoid. Which of the following is true? a) the electron will be accelerated along the axis b) the electron path will be circular about the axis c) the electron will experience a force at 45o to the axis and hence execute a helical path d) the electron will continue to move with uniform velocity along the axis of the solenoid
d) the electron will continue to move with uniform velocity along the axis of the solenoid
A current circular loop of radius R is placed in the x-y plane with centre at the origin. Half of the lop with x > 0 is now bent so that it now lies in the y-z plane. a) the magnitude of magnetic moment now diminishes b) the magnetic moment does not change c) the magnitude of B at (0,0,z),z >> R increases d) the magnitude of B at (0,0,z),z >> R is unchanged
a) the magnitude of magnetic moment now diminishes
Biot-Savart law indicates that the moving electrons produce a magnetic field B such that a) B ┴ v b) B ‖ v c) it obeys inverse cube law d) it is along the line joining the electrons and point of observation
a) B ┴ v
Two charged particles traverse identical helical paths in an opposite sense in a uniform magnetic field a) they have equal z-components of momenta b) they must have equal charges c) they necessarily represent a particle-antiparticle pair d) the charge to mass ratio satisfy: (e/m)1 + (e/m)2 = 0
d) the charge to mass ratio satisfy: (e/m)1 + (e/m)2 = 0
There are two current-carrying planar coils made each from identical wires of length L. C1 is circular and C2 is square. They are so constructed that they have the same frequency of oscillation when they are placed in the same uniform B and carry the same current. Find a in terms of R.
The circular coil C1 has a radius of R, a length of L, and a number of turns per unit length of n1 = L/2R. The square C2 has a side, a perimeter, and a number of turns per unit length of n2 = L/4a....
Consider the plane S formed by the dipole axis and the axis of the earth. Let P be a point on the magnetic equator and in S. Let Q be the point of intersection of the geographical and magnetic equators. Obtain the declination and dip angle at P and Q.
The declination is zero, P is in the plane, S is in the north, and P is in the plane. The declination for point P is 0 since it is in the plane S created by the dipole axis and the earth's axis....
Assume the dipole model for earth’s magnetic field B which is given by Bv = vertical component of magnetic field = μ0/4π 2m cos θ/r3, BH = horizontal component of magnetic field = μ0/4π 2m sin θm/r3, θ = 90o latitude as measured from magnetic equator. Find loci of points for which i) |B| is minimum ii) dip angle is zero, and iii) dip angle is ±45o.
a) |B| is minimum at the magnetic equator. b) Angle of dip is zero when θ = π/2 c) When dip angle is ±45o θ = tan-1 is the locus.
What are the dimensions of χ, the magnetic susceptibility? Consider an H-atom. Guess an expression for χ, up to a constant by constructing a quantity of dimensions of χ, out of parameters of the atom: e, m, v, R and μ0. Here, m is the electronic mass, v is electronic velocity, R is Bohr radius. Estimate the number so obtained and compare with the value of | χ| equivalent to 10-5 for many solid materials.
χm = I/H = intensity of magnetisation/magnetising force χ is dimensionless as I and H has the same units χ = 10-4
Verify the Ampere’s law for the magnetic field of a point dipole of dipole moment Take C as the closed curve running clockwise along i) the z-axis from z = a > 0 to z = R; ii) along the quarter circle of radius R and centre at the origin, in the first quadrant of x-z plane; iii) along the x-axis from x = R to x = a and iv) along the quarter circle of radius a and centre at the origin in the first quadrant of the x-z plane.
Magnetic field = 0M/4(1/a2-1/R2) along the z-axis b) On the circular arc, the magnetic field at point A is = 0m/4R2. c) (d) The magnetic moment is 0
Use i) the Ampere’s law for H and ii) continuity of lines of B, to conclude that inside a bar magnet a) lines of H run from the N pole to S pole, while b) lines of B must run from the S pole to N pole.
The amperian loop is denoted by the letter C. We can find the angle between the two points by solving the above equation. cos is negative because it is greater than 90o.
In three moles of ethane (C2H6), calculate the following: (i) Number of moles of carbon atoms. (ii) Number of moles of hydrogen atom (iii) Number of molecules of ethane
(a) 1 mole ${{C}_{2}}{{H}_{6}}$ contains two moles of C- atoms. ∴∴ No. of moles of C- atoms in 3 moles of ${{C}_{2}}{{H}_{6}}$ = 2 * 3 = 6 (b) 1 mole ${{C}_{2}}{{H}_{6}}$ contains six moles of H-...
Calculate the atomic mass (average) of chlorine using the following data:
Average atomic mass of Cl. = $[(\text{Fractional abundance of }\!\!~\!\!\text{ }_{{}}^{35}Cl)(\text{molar mass of }\!\!~\!\!\text{ }_{{}}^{35}Cl)+(\text{fractional abundance of }\!\!~\!\!\text{...
Determine the molecular formula of an oxide of iron, in which the mass percent of iron and oxygen are 69.9 and 30.1, respectively.
Mass percent of Fe = 69.9% Mass percent of O = 30.1% No. of moles of Fe present in oxide =$ \frac{69.90}{55.85}$ = 1.25 No. of moles of O present in oxide =$\frac{30.1}{16.0}$ =1.88 Ratio of Fe to...
How much copper can be obtained from 100 g of copper sulphate (CuSO4)?
1 mole of $CuSO_{4}$ contains 1 mole of Cu. Molar mass of $CuSO_{4}$ = (63.5) + (32.00) + 4(16.00) = 63.5 + 32.00 + 64.00 = 159.5 grams 159.5 grams of $CuSO_{4}$ contains 63.5 grams of Cu....
Calculate the concentration of nitric acid in moles per litre in a sample which has a density, 1.41 g mL–1 and the mass per cent of nitric acid in it being 69%
Mass percent of HNO3 in sample is 69 % Thus, 100 g of HNO3 contains 69 g of HNO3 by mass. Molar mass of HNO3 = { 1 + 14 + 3(16)} g.mol^{-1}g.mol−1 = 1 + 14 + 48 = 63g mol^{-1}=63gmol−1 Now,...
Calculate the mass of sodium acetate 
required to make 500 mL of 0.375 molar aqueous solution. Molar mass of sodium acetate is 82.0245 g mol–1.
0.375 Maqueous solution of $CH_{3}COONa$ = 1000 mL of solution containing 0.375 moles of $CH_{3}COONa$ Therefore, no. of moles of $CH_{3}COONa$ in 500 mL = 0.1875 mole Molar mass of sodium acetate...
Calculate the amount of carbon dioxide that could be produced when (i) 1 mole of carbon is burnt in air. (ii) 1 mole of carbon is burnt in 16 g of dioxygen. (iii) 2 moles of carbon are burnt in 16 g of dioxygen.
(i) 1 mole of carbon is burnt in air. $C+{{O}_{2}}\to C{{O}_{2}}$ 1 mole of carbon reacts with 1 mole of O2 to form one mole of CO2. Amount of $CO_{2}$ produced = 44 g (ii) 1 mole of carbon...
Determine the empirical formula of an oxide of iron, which has 69.9% iron and 30.1% dioxygen by mass.
Percentage of Fe by mass = 69.9% [As said previously] By mass, 30.1 percent of O2 is present. [As said previously] Relative moles of Fe in iron oxide: = (69.9)x(55.85}/55.8569.9 = 1.25 Relative...
Calculate the mass per cent of different elements present in sodium sulphate 
Now for Na2SO4. Molar mass of Na2SO4 = [(2 x 23.0) + (32.066) + 4(16.00)] =142.066 g Therefore, mass percent of the sodium element: = 32.379 = 32.4% Mass percent of the sulphur element: = 22.57...