Login/Sign Up
Home » ICSE » Class 12 » Selina » Physics
Physics

The figure shown a two-slit arrangement with a source which emits unpolarised light. P is a polariser with axis whose direction is not given. If I0 is the intensity of the principal maxima when no polarizer is present, calculate in the present case, the intensity of the principal maxima as well as of the first minima.

, , , ,

Given wave amplitude in perpendicular polarisation $ A_{\perp}=A_{\perp}^{0}(\sin (k x-\omega t)+\sin (k x-\omega t+\phi)) $ wave amplitude in parallel polarisation $ A_{\|}=A_{\|}^{0}(\sin (k...

read more

AC = CO = D, S1 C = S2 C = d << D A small transparent slab containing material of µ =1.5 is placed along AS2. What will be the distance from O of the principal maxima and of the first minima on either side of the principal maxima obtained in the absence of the glass slab?

, , , ,

According to the question, $ \begin{array}{l} \Delta x=2 d \sin \theta+(\mu-1) L \\ \sin \theta 0=-1 / 16 \end{array} $ From central maxima, $O P=-D / 16$ $ \sin \theta_{1}=\frac{\pm \lambda / 2-d /...

read more

A helicopter of mass 2000 kg rises with a vertical acceleration of 15 m/s2. The total mass of the crew and passengers is 500 kg. Give the magnitude and direction of the a) force on the floor of the helicopter by the crew and passengers b) action of the rotor of the helicopter on the surrounding air c) force on the helicopter due to the surrounding air

, , , ,

Given, M = 2000 kg helicopter mass m = 500 kg m = 500 kg m = 500 kg m = 500 kg m = 500 kg m = 500 kg Helicopter acceleration with crew and passengers = 15 m/s2 a) Force exerted by the crew and...

read more

A rectangular box lies on a rough inclined surface. The coefficient of friction between the surface and the box is μ. Let the mass of the box be m. a) at what angle of inclination θ of the plane to the horizontal will the box just start to slide down the plane? b) what is the force acting on the box down the plane, if the angle of inclination of the plane is increased to a > θ c) what is the force needed to be applied upwards along the plane to make the box either remain stationary or just move up with uniform speed? d) what is the force needed to be applied upwards along the plane to make the box move up the plane with acceleration a.

, , , ,

a) As the box starts to slide down the plane, $\mu=\tan \theta$ $ \theta=\tan ^{-1}(\mu) $ b) If $a>\theta$, the angle of inclination will be the angle of repose and the net force acting will be...

read more

A cricket bowler releases the ball in two different ways a) giving it only horizontal velocity and b) giving it horizontal velocity and a small downward velocity. The speed vs at the time of release is the same. Both are released at a height H from the ground. Which one will have greater speed when the ball hits the ground? Neglect air resistance.

, , , ,

a) $\frac{1}{2} v_{z}^{2}=g H \Rightarrow v_{z}=\sqrt{2 g H}$ Speed at ground is given as: $\sqrt{v_{s}^{2}+v_{z}^{2}}=\sqrt{v_{s}^{2}+2 g H}$ b)$\frac{1}{2} m v_{s}^{2}+m g H$ is the total energy...

read more

A racing car travels on a track ABCDEFA. ABC is a circular arc of radius 2 R. CD and FA are straight paths of length R and DEF is a circular arc of radius R = 100 m. The coefficient of friction on the road is μ = 0.1. The maximum speed of the car is 50 m/s. Find the minimum time for completing one round.

, , , ,

Time taken from $A$ to $B$ to $C$ $\mathrm{S} 1=$ length $\mathrm{pf}$ path $=3 / 42 \pi(2 \mathrm{R})=300 \pi \mathrm{m}$ $\mathrm{V} 1=$ speed(maximum) along the circular path of the car $...

read more

When a body slides down from rest along a smooth inclined plane making an angle of 45 degree with the horizontal, it takes time T. When the same body slides down from rest along a rough inclined plane making the same angle and through the same distance, it is seen to take time pT, where p is some number greater than 1. Calculate the coefficient of friction between the body and the rough plane.

, , , ,

The inclined plane angle is $45^{\circ}$ such that $ \begin{array}{l} u=0 \\ s=s \\ t=T \\ a=g \sin 45^{\circ}=g / \sqrt{2} \\ s=u t+1 / 2 a t^{2} \\ s=g T^{2} / 2 \sqrt{2} \end{array} $ $...

read more

There are three forces F1, F2, and F3 acting on a body, all acting on a point P on the body. The body is found to move with uniform speed. a) show that the forces are coplanar b) show that the torque acting on the body about any point due to these three forces is zero

, , , ,

a) The body's acceleration is zero because the resultant force of the three forces F1, F2, and F3 on a location on the body is zero. The directions of forces F1 and F2 are in the plane of the paper,...

read more

A bock of mass M is held against a rough vertical wall by pressing it with a finger. If the coefficient of friction between the block and the wall is μ and the acceleration due to gravity is g, calculate the minimum force required to be applied by the ginger to hold the block against the wall?

, , , ,

F is the force exerted by the finger on a body of mass M that is resting on the wall. Using the balanced state as a starting point, $ \begin{array}{l} \mathrm{F}=\mathrm{N} \\ \mathrm{f}=\mathrm{Mg}...

read more

Block A of weight 100N rests on a frictionless inclined plane of slope angle 30o. A flexible cord attached to A passes over a frictionless pulley and is connected to block B of weight W. Find the weight W for which the system is in equilibrium.

, , , ,

Equilibrium between $A$ or $B$, Then we know that, $\mathrm{mg} \sin 30^{\circ}=\mathrm{F}$ $ \begin{array}{l} 1 / 2 \mathrm{mg}=\mathrm{F} \\ \mathrm{F}=(1 / 2)(100)=50 \end{array} $ Therefore,...

read more

A mass of 2 kg is suspended with thread AB. Thread CD of the same type is attached to the other end of 2 kg mass. Lower thread is pulled gradually harder and harder in the downward direction so as to apply force on AB. Which of the threads will break and why?

, , , ,

As the mass 2 kg acts downward, the force acting on the thread AB is equal to the force F. As a result, the force exerted on the AB is 2 kg more than on the D, and the thread AB breaks.

read more

Consider a light beam incident from air to a glass slab at Brewster’s angle as shown in the figure.A polaroid is placed in the path of the emergent ray at point P and rotated about an axis passing through the centre and perpendicular to the plane of the polaroid (a) For a particular orientation, there shall be darkness as observed through the polaroid (b) The intensity of light as seen through the polaroid shall be independent of the rotation (c) The intensity of light as seen through the Polaroid shall go through a minimum but not zero for two orientations of the polaroid (d) The intensity of light as seen through the polaroid shall go through a minimum for four orientations of the polaroid

, , , ,

The correct answer is c) The intensity of light as seen through the Polaroid shall go through a minimum but not zero for two orientations of the polaroid

read more

In a Young’s double-slit experiment, the source is white light. One of the holes is covered by a red filter and another by a blue filter. In this case (a) there shall be alternate interference patterns of red and blue (b) there shall be an interference pattern for red distinct from that for blue (c) there shall be no interference fringes (d) there shall be an interference pattern for red mixing with one for blue

, , , ,

The correct answer is c) there shall be no interference fringes

read more

The figure shows a standard two-slit arrangement with slits S1, S2. P1, P2 are the two minima points on either side of P. At P2 on the screen, there is a hole and behind P2 is a second 2- slit arrangement with slits S3, S4 and a second screen behind them;(a) There would be no interference pattern on the second screen but it would be lighted (b) The second screen would be totally dark (c) There would be a single bright point on the second screen (d) There would be a regular two-slit pattern on the second screen

, , , ,

The correct answer is d) there would be a regular two-slit pattern on the second screen

read more

Two sources S1 and S2 of intensity I 1 and I 2 are placed in front of a screen in the figure (a). The pattern of intensity distribution seen in the central portion is given by the figure (b). In this case which of the following statements are true;(a) S1 and S2 have the same intensities (b) S1 and S2 have a constant phase difference (c) S1 and S2 have the same phase (d) S1 and S2 have the same wavelength.

, , , ,

The correct answer is a) S1 and S2 have the same intensities b) S1 and S2 have a constant phase difference c) S1 and S2 have the same phase

read more

The human eye has an approximate angular resolution of φ = 5.8 × 10–4 rad and a typical photo printer prints a minimum of 300 dpi (dots per inch, 1 inch = 2.54 cm). At what minimal distance z should a printed page be held so that one does not see the individual dots.

, , , ,

Angular separation, φ = 5.8 × 10–4 rad The average distance between the two dots = 2.54/300 = 0.85 × 10-2 cm At distance z cm, the angle subtended = 0.85 × 10-2/z Resolution angle for human = 0.85 ×...

read more

A polaroid (I) is placed in front of a monochromatic source. Another polaroid (II) is placed in front of this polaroid (I) and rotated till no light passes. A third polaroid (III) is now placed in between (I) and (II). In this case, will light emerge from (II)? Explain.

, , , ,

A monochromatic source is placed in front of polaroid (I), and polaroid (II) is positioned in front of polaroid (I) (I). The light is unaltered as it travels through the polaroid (II). The Polaroid...

read more

Consider a two-slit interference arrangements such that the distance of the screen from the slits is half the distance between the slits. Obtain the value of D in terms of λ such that the first minima on the screen falls at a distance D from the centre O.

, , , ,

The minima will occur when ∆x = S2P – S1P = (2n-1/2)λ S1P = √D2 + (D – x)2 S2P = √D2 + (D + x)2 T2P = D + x T1P = D – x [D2 + (D+x)2]-1/2 – [D2+(D-x)2]1/2 = λ/2   D =...

read more

Four identical monochromatic sources A, B, C, D as shown in the figure produce waves of the same wavelength λ and are coherent. Two receiver R1 and R2 are at great but equal distances from B. (i) Which of the two receivers picks up the larger signal? (ii) Which of the two receivers picks up the larger signal when B is turned off? (iii) Which of the two receivers picks up the larger signal when D is turned off? (iv) Which of the two receivers can distinguish which of the sources B or D has been turned off?

, , , ,

i) R2 is the larger signal. ii) When B is switched off, R1 is y = a cos ꞷt IR1 = a2/2 R2 is y = a cos ꞷt IR2 = a2/2 So, it can be said that R1 and R2 are the same. iii) When D is switched off, R1 is...

read more

The optical properties of a medium are governed by the relative permittivity (εr) and relative permeability (µr ). The refractive index is defined as √µr εr = n. For ordinary material εr > 0 and µr > 0 and the positive sign is taken for the square root. In 1964, a Russian scientist V. Veselago postulated the existence of material with εr < 0 and µr < 0. Since then such ‘metamaterials’ have been produced in the laboratories and their optical properties studied. For such materials n = -√µrεr. As light enters a medium of such refractive index the phases travel away from the direction of propagation. (i) According to the description above show that if rays of light enter such a medium from the air (refractive index =1) at an angle θ in 2nd quadrant, them the refracted beam is in the 3rd quadrant (ii) Prove that Snell’s law holds for such a medium

, , , ,

BC = √μrεr (CD-AE) BC >0; CD > AE -√μrεr AE = BC – √μrεr CD BC = √μrεr (CD – AE) AE > CD Therefore, BC < 0 ii) BC = AC sin θi CD – AE = AC sin θr BC = √μrεr AC sin θi = √μrεr AC sin θr...

read more

To ensure almost 100 per cent transmissivity, photographic lenses are often coated with a thin layer of dielectric material. The refractive index of this material is intermediated between that of air and glass (which makes the optical element of the lens). A typically used dielectric film is MgF2 (n = 1.38). What should the thickness of the film be so that at the centre of the visible spectrum (5500 Ao) there is maximum transmission?

, , , ,

IA is incident at point A, forming an incident angle I between the air and the film surface. The reflected and refracted rays are AR1 and AD, respectively. D is the point where the partial...

read more

Consider a 20 W bulb emitting light of wavelength 5000 A ° and shining on a metal surface kept at a distance 2m. Assume that the metal surface has work function of 2 eV and that each atom on the metal surface can be treated as a circular disk of radius 1.5 A ° . (i) Estimate no. of photons emitted by the bulb per second. [Assume no other losses] (ii) Will there be photoelectric emission? (iii) How much time would be required by the atomic disk to receive energy equal to work function (2 eV)? (iv) How many photons would atomic disk receive within time duration calculated in (iii) above? (v) Can you explain how photoelectric effect was observed instantaneously?

, , , ,

Given, P = 20W λ = 5000 Ao = 5000 × 10-10 m d = 2m ϕ0 = 2 eV r = 1.5 × 10-10 m No.of photon emitted per second by the bulb = n’ = dN/dt i) No.of photon emitted by bulb per second = n’ = p λ/hc = 5 ×...

read more

A particle A with a mass mA is moving with a velocity v and hits a particle B (mass mB) at rest (one dimensional motion). Find the change in the de Broglie wavelength of the particle A. Treat the collision as elastic.

, , , ,

According to the law of conservation of momentum, mAv + mB0 = mAv1 + mBv2 mA(v-v1) = mBv2 1/2 mAv2 = 1/2 mAv12 + 1/2mBv22 mA(v-v1)(v+v1) = mBv22 v1 = (mA-mB/mA+mB)v v2 = (2mA/mA+mB)v λinitial =...

read more

A student performs an experiment on the photoelectric effect, using two materials A and B. A plot of Vstop vs ν is given in the figure. (i) Which material A or B has a higher work function? (ii) Given the electric charge of an electron = 1.6 × 10–19 C, find the value of h obtained from the experiment for both A and B. Comment on whether it is consistent with Einstein’s theory

, , , ,

i) The threshold frequency of A is vOA = 5 × 1014 Hz The threshold frequency of B is vOB = 10 × 1014 Hz Work function is ϕ = hv0 ϕOA/ ϕOB = 5 × 1014/10 × 1014 < 1 ϕOA <...

read more

Consider an electron in front of the metallic surface at a distance d (treated as an infinite plane surface). Assume the force of attraction by the plate is given as 2 2 0 1 4 4 q πε d Calculate work in taking the charge to an infinite distance from the plate. Taking d = 0.1nm, find the work done in electron volts. [Such a force law is not valid for d < 0.1nm].

, , , ,

An electron is progressively moved in the picture. The distance travelled by the electron is x, and this is accomplished by the application of an external force. F = q2/4×4πε0d2 d = 0.1 nm = 10-10 m...

read more

Consider a thin target (10^{-2}m square, 10^{-3}m thickness) of sodium, which produces a photocurrent of 100µA when a light of intensity 100W/m2 (λ = 660nm) falls on it. Find the probability that a photoelectron is produced when a photon strikes a sodium atom. [Take density of Na = 0.97 kg/m3].

, , , ,

Area = 10-4 m2 Thickness = 10-3 m Current = 10-4 A Intensity = 100 W/m2 Mass = (volume)(density) = 0.97 × 10-4 gm No.of target atoms = 0.254 × 1019 Total energy = nhv Where n = 3.3 × 1016 The...

read more

Two particles A and B of de Broglie wavelengths λ1 and λ2 combine to form a particle C. The process conserves momentum. Find the de Broglie wavelength of the particle C. (The motion is one dimensional).

, , , ,

By de-Broglie wavelengths, λ=h/p p=h/ λ p1 = h/ λ1 p2 = h/ λ2 p3 = h/ λ3 There are 4 possible cases and they are: Case 1: When p1 and p2 are positive, then λ3 = λ1 λ1/ λ1+ λ2 Case 2: When p1 and p2...

read more

There are two sources of light, each emitting with a power of 100 W. One emits X-rays of wavelength 1nm and the other visible light at 500 nm. Find the ratio of a number of photons of X-rays to the photons of visible light of the given wavelength?

, , , ,

Ex = hvx Ev = hvv Let nx and nv be the no.of photons from x-rays and visible light are of equal energies and they emit 100 W power. nxhvx = nvhvv nx/nv = vv/vx = λx/λv nx/nv = 1 nm/500 nm nx:nv =...

read more

(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...

read more

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...

read more

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

read more

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

read more

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...

read more

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

read more

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

read more

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 \mu =\frac{\sin {{\theta }_{2}}-\sin {{\theta }_{1}}}{\cos {{\theta }_{1}}}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...

read more

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

read more

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...

read more

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...

read more

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

read more

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

read more

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

read more

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....

read more

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

read more

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

read more

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...

read more

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

read more

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

read more

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

read more

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...

read more

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...

read more

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...

read more

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

read more

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...

read more

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

read more

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 × {10}^{4} N d) 2.1 \times {10}^{4}N

, , , ,

c) 1.05 × 104 N

read more

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

read more

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

read more

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

read more

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...

read more

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...

read more

Consider a circular current-carrying loop of radius R in the x-y plane with centre at the origin. Consider the line integral\Im (L)=\left| \left. \int_{-L}^{L}{B.dl} \right| \right.a) show that\Im (L)monotonically increases with L b) use an appropriate Amperian loop to that\Im (\infty )={{\mu }_{0}}Iwhere 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\Im (\infty )\text{and }\Im \text{(L)}

, , , ,

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:...

read more

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 =...

read more

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...

read more

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

read more

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...

read more

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...

read more

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

read more

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 \({{\vec{B}}_{net}}=\frac{1}{4}\left( \frac{{{\mu }_{0}}I}{2R} \right)(\widehat{i}+\widehat{j}+\widehat{k})\)

read more

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

read more

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

read more

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

read more

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....

read more

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....

read more

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.

read more

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

read more

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

read more

A bar magnet of magnetic moment m and moment of inertia I is cut into two equal pieces, perpendicular to length. Let T be the period of oscillations of the original magnet about an axis through the midpoint, perpendicular to the length, in a magnetic field B. What would be the similar period T’ for each piece?

, , , ,

T stands for the time period. The moment of inertia is me. The magnet's mass is m. B stands for magnetic field. T = 2I/MB M' = M/2 magnetic dipole moment T' = T/2 is the time period.

read more

Essential difference between electrostatic shielding by a conducting shell and magneto static shielding is due to a) electrostatic field lines can end on charges and conductors have free charges b) lines of B can also end but conductors cannot end them c) lines of B cannot end on any material and perfect shielding is not possible d) shells of high permeability materials can be used to divert lines of B from the interior region

, , , ,

a) electrostatic field lines can end on charges and conductors have free charges c) lines of B cannot end on any material and perfect shielding is not possible d) shells of high permeability...

read more

A long solenoid has 1000 turns per meter and carries a current of 1 A. It has a soft iron core of μr = 1000. The core is heated beyond the Curie temperature Tc a) the H field in the solenoid is unchanged but the B field decreases drastically b) the H and B fields in the solenoid are nearly unchanged c) the magnetisation in the core reverses direction d) the magnetisation in the core diminishes by a factor of about 108

, , , ,

a) the H field in the solenoid is unchanged but the B field decreases drastically d) the magnetisation in the core diminishes by a factor of about 108

read more

Consider the two idealized systems: i) a parallel plate capacitor with large plates and small separation and ii) a long solenoid of length L >> R, the radius of the cross-section. In i) E is ideally treated as a constant between plates and zero outside. In ii) magnetic field is constant inside the solenoid and zero outside. These idealised assumptions, however, contradict fundamental laws as below: a) case (i) contradicts Gauss’s law for electrostatic fields b) case (ii) contradicts Gauss’s law for magnetic fields c) case (i) agrees withd) case (ii) contradicts

, , , ,

b) In the case of magnetic fields, instance (ii) violates Gauss's law.

read more

The magnetic field of the earth can be modelled by that of a point dipole placed at the centre of the earth. The dipole axis makes an angle of 11.3o with the axis of the earth. At Mumbai, declination is nearly zero. Then, a) the declination varies between 11.3o W to 11.3o E b) the least declination is 0o c) the plane defined by dipole axis and the earth axis passes through Greenwich d) declination average over the earth must be always negative

, , , ,

a) The declination ranges from 11.3 degrees West to 11.3 degrees East.

read more

A toroid of n turns, mean radius R and cross-sectional radius a carries current I. It is placed on a horizontal table taken as an x-y plane. Its magnetic moment m a) is non-zero and points in the z-direction by symmetry b) points along the axis of the toroid c) is zero, otherwise, there would be a field falling as 1/r3 at large distances outside the toroid d) is pointing radially outwards

, , , ,

c) is zero; otherwise, a field dropping as 1/r3 at great distances outside the toroid would exist.

read more

A long solenoid ‘S’ has ‘n’ turns per meter, with diameter ‘a’. At the centre of this coil, we place a smaller coil of ‘N’ turns and diameter ‘b’ (where b < a). If the current in the solenoid increases linearly, with time, what is the induced emf appearing in the smaller coil. Plot graph showing nature of variation in emf, if current varies as a function of mt2 + C.

, , , ,

The solenoid's changing magnetic field is represented as: onI = B1(t) (t) The second coil's magnetic flux is 2 = onI(t).b2 As a result of the solenoid's changing magnetic field, the induced emf in...

read more

A metallic ring of mass m and radius l (ring being horizontal) is falling under gravity in a region having a magnetic field. If z is the vertical direction, the z-component of the magnetic field is Bz = Bo (1+λ z). If R is the resistance of the ring and if the ring falls with a velocity v, find the energy lost in the resistance. If the ring has reached a constant velocity, use the conservation of energy to determine v in terms of m, B, λ and acceleration due to gravity g.

, , , ,

v = mgR/B02π2λ2l4

read more

A rod of mass m and resistance R slides smoothly over two parallel perfectly conducting wires kept sloping at an angle θ with respect to the horizontal. The circuit is closed through a perfect conductor at the top. There is a constant magnetic field B along the vertical direction. If the rod is initially at rest, find the velocity of the rod as a function of time.

, , , ,

The angle formed by B and PQ is 90 dϕ = B.dA dϕ = B v d cos θ -ε = B v d cos θ I = -Bvd/R cos θ Using Newton's second law to solve the preceding problem, we get v as v = α g sin θ [1 – e...

read more