NEET

A nucleus of uranium decays at rest into nuclei of thorium and helium. Then: (1) The helium nucleus has less kinetic energy than the thorium nucleus (2) The helium nucleus has more kinetic energy than the thorium nucleus (3) The helium nucleus has less momentum then the thorium nucleus. (4) The helium nucleus has more momentum than the thorium nucleus

The correct Solution is (2) $ \begin{array}{l} \mathrm{U} \rightarrow \mathrm{Th}+\alpha \\ \mathrm{KE}_{\mathrm{Th}}=\frac{\mathrm{P}^{2}}{2 \mathrm{~m}_{\mathrm{Th}}},...

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Point masses \mathrm{m}_{1} and \mathrm{m}_{2} are placed at the opposite ends of rigid rod of length \mathrm{L}, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity \omega_{0} is minimum, is given by:(1) \mathrm{x}=\frac{\mathrm{m}_{2} \mathrm{~L}}{\mathrm{~m}_{1}+\mathrm{m}_{2}} (2) x=\frac{m_{1} L}{m_{1}+m_{2}} (3) \mathrm{x}=\frac{\mathrm{m}_{1}}{\mathrm{~m}_{2}} \mathrm{~L} (4) \mathrm{x}=\frac{\mathrm{m}_{2}}{\mathrm{~m}_{1}} \mathrm{~L}

Solution: (1) $ \mathrm{K} . \mathrm{E} .=\frac{1}{2} \mathrm{I} \omega^{2} $ I is min. about the centre of mass $So,\left(m_{1}\right)(x)=\left(m_{2}\right)(L-x)$ $ \mathrm{x}=\frac{\mathrm{m}_{2}...

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The position vector of a particle \overrightarrow{\mathrm{R}} as a function of time is given by: \overline{\mathrm{R}}=4 \sin (2 \pi t) \hat{1}+4 \cos (2 \pi t)]Where \mathrm{R} is in meters, \mathrm{t} is in seconds and Î and j denote unit vectors along \mathrm{x} – and \mathrm{y}-directions, respectively. Which one of the following statements is wrong for the motion of particle? (1) Patch of the particle is a circle of radius 4 meter (2) Acceleration vector is along -\overline{\mathrm{R}} (3) Magnitude of acceleration vector is \frac{v^{2}}{R}, where v is the velocity of particle (4) Magnitude of the velocity of particle is 8 meter/second,

The correct Solution is (4) $ \begin{array}{l} \mathrm{x}=45 \mathrm{~m} 2 \pi \mathrm{t} \\ \mathrm{y}=4 \cos (2 \pi \mathrm{t}) \end{array} $ On Squaring and adding. $\Rightarrow$ Circular motion...

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A satellite \mathrm{S} is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then, (1) The acceleration of $ is always directed towards the centre of the earth (2) The angular momentum of \mathrm{S} about the centre of the earth changes in direction, but its magnitude remains constant. (3) The total mechanical energy of S varies periodically with time (4) The linear momentum of S remains constant is magnitude

The correct Solution is (1) and (2) The gravitational pull on the satellite will be directed toward the centre of the earth, hence the satellite's acceleration will also be directed toward the...

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A rectangular coil of length 0.12 \mathrm{~m} and width 0.1 \mathrm{~m} having 50 turns of wire is suspended vertically in a uniform magnetic field of strength 0.2 Weber / \mathrm{m}^{2}. The coil carries a current of 2 \mathrm{~A}. if the plane of the coil is inclined at an angle of 30^{\circ} with the direction of the field, the torque required to keep coil in stable equilibrium will be: (1) 0.12 \mathrm{Nm} (2) 0.15 \mathrm{Nm} (3) 0.20 \mathrm{Nm} (4) 0.24 \mathrm{Nm}.

The correct solution is (3) $ \begin{array}{l} \vec{\tau}=\overrightarrow{\mathrm{M}} \times \overline{\mathrm{B}}=\mathrm{MB} \sin 60^{\circ} \\ =\mathrm{Ni} \mathrm{AB} \sin 60^{\circ} \\ 50...

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A source of sound S emitting waves of frequency 100 \mathrm{~Hz} and an observer \mathrm{O} are located at some distance from each other. The source is moving with a speed of 19.4 \mathrm{~ms}^{-1} at an angle of 60^{\circ} with the source observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air 330 \mathrm{~ms}^{-1} ), is: (1) 97 \mathrm{~Hz} (2) 100 \mathrm{~Hz} (3) 103 \mathrm{~Hz} (4) 106 \mathrm{~Hz}

The correct solution is (3)   $ \begin{array}{l} t^{1}=f_{0}\left(\frac{v-v}{v-v_{s}}\right) \\ f^{1}=100\left(\frac{v-0}{v-(+9.7)}\right) \\ f^{1}=100 \frac{v}{v\left(1-\frac{9.7}{V}\right)}...

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An infinitely long straight conductor carries a current of 5 A as shown. An electron is moving with a speed of 105 m/s parallel to the conductor. The perpendicular distance between the electron and the conductor is 20 cm at an instant. Calculate the magnitude of the force experienced by the electron at that instant.

(1) 4 × 10–20 N                                         (2) 8π × 10–20 N (3) 4π × 10–20 N                                       (4) 8 × 10–20 N Solution: Answer (4) The magnetic field produced due...

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A long solenoid of diameter 0.1 m has 2 × 104 turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is 1000 ohms, the total charge flowing through the coil during this time is

(1) 16 micro Columb                    (2) 32 micro Columb (3) 16 pi micro Columb                (4) 32 pi micro Columb Solution: Answer (2) According to the question, Number of turns, n=100...

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 A U tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is

(1) 425 kg m–3                     (2) 800 kg m–3 (3) 928 kg m–3                    (4) 650 kg m–3 Solution: Answer (3) $ {{h}_{oil}}{{\rho }_{oil}}g={{h}_{water}}{{\rho }_{water}}g $ $ 140\times...

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Suppose the charge of a proton and an electron differ slightly. One of them is –e, the other is (e + e). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then e is of the order of [Given mass of hydrogen mh = 1.67 × 10–27 kg]

(1) 10–23 C                                   (2) 10–37 C (3) 10–47 C                                   (4) 10–20 C Solution: Answer (2)...

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A beam of light from a source L is incident normally on a plane mirror fixed at a certain distance x from the source. The beam is reflected back as a spot on a scale placed just above the source L. When the mirror is rotated through a small angle theta, the spot of the light is found to move through a distance y on the scale. The angle theta is given by

(1) y/x (2) x/2y (3) x/y (4) y/2x Solution: Answer (4) When mirror is rotated by an angle theta, reflected ray will be rotated by an angle twice that of theta. $ \frac{y}{x}=2\theta  $ $ \theta...

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Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities 1 and 2. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is

          Solution: C $ Let\text{ }the\text{ }angular\text{ }velocity\text{ }of\text{ }the\text{ }combination\text{ }be\text{ }W $ $ conservation\text{ }of\text{...

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Figure shows a circuit contains three identical resistors with resistance R = 9.0 ohms each, two identical inductors with inductance L = 2.0 mH each, and an ideal battery with emf= 18 V. The current ‘i’ through the battery just after the switch closed is

(1) 0.2 A                             (2) 2 A (3) 0 ampere                    (4) 2 mA Solution: Answer (2) At t = 0, no current flows through R1 and R3 \ I = e/R2 =18 / 9 = 2...

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One end of string of length l is connected to a particle of mass ‘m’ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed ‘v’, the net force on the particle (directed towards center) will be (T represents the tension in the string)

$ (1)\,\,T+\frac{m{{v}^{2}}}{l} $ $ (2)\,\,T-\frac{m{{v}^{2}}}{l} $ $ (3)\,\,Zero $ $ (4)\,\,T $ Solution: Answer (4) N=mg & T is the tension. Because tension provides centripetal force, the net...

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Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t1. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t2. The time taken by her to walk up on the moving escalator will be

$ (1)\,\,\frac{{{t}_{1}}{{t}_{2}}}{{{t}_{2}}-{{t}_{1}}} $ $ (2)\,\,\frac{{{t}_{1}}{{t}_{2}}}{{{t}_{2}}+{{t}_{1}}} $ $ (3)\,\,{{t}_{1}}-{{t}_{2}} $ $ (4)\,\,\frac{{{t}_{1}}+{{t}_{2}}}{2} $ Solution:...

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Two cars moving in opposite directions approach each other with speed of 22 m/s and 16.5 m/s respectively. The driver of the first car blows a horn having a frequency 400 Hz. The frequency heard by the driver of the second car is [velocity of sound 340 m/s]

(1) 361 Hz                                         (2) 411 Hz (3) 448 Hz                                         (4) 350 Hz Solution: Answer (3) $ {{f}_{A}}=f\left[ \frac{v+{{v}_{0}}}{v-{{v}_{0}}}...

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An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 ms-1 and the second part of mass 2Kg moves with 8 ms-1 speed. If the third part files off with 4 ms-1 speed, then its mass is

Option A 17 kg Option B 3 kg Option C 5 kg Option D 7 kg Solution: Correct Option C Just before and after the explosion Momentum of the system will be conserved. This conclusion follows from the law...

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