Physics - Systems Particles Rotational Motion - Quiz-11

Internal forces cannot change:

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the kinetic energy of a system.
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the mechanical energy of a system.
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the momentum of a system.
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all of these

One sphere collides with another sphere of double its mass. While heavier mass was at rest initially. The ratio of their respective speeds after the collision will be (Coefficient of restitution = e)

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$\frac{1 - 2 e}{1 - e}$
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$\frac{1 - 2 e}{1 + e}$
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$\frac{1 - e}{1 + 2 e}$
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$\frac{1 + 2 e}{1 - e}$

A particle of mass $m_{1}$ makes an elastic, one-dimensional collision with another stationary particle of mass $m_{2}$ . The fraction of kinetic energy of $m_{1}$ carried away by $m_{2}$ is

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$\frac{m_{1}^{2}}{m_{2}^{2}}$
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${(\frac{m_{1}^{2}}{m_{2}^{2}})}^{- 1}$
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$\frac{m_{1} - m_{2}}{{(m_{1} + m_{2})}^{2}}$
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$\frac{4 m_{1} m_{2}}{{(m_{1} + m_{2})}^{2}}$

Two particles moving initially in the same direction undergo a one-dimensional elastic collision. Their relative velocities before and after the collision are ${\vec{v}}_{1} and {\vec{v}}_{2}$ . Which of the following is not correct?

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$|{\vec{v}}_{1}| = |{\vec{v}}_{2}|$
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${\vec{v}}_{1} = - {\vec{v}}_{2}$ only is the two are of equal mass
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${\vec{v}}_{1} . {\vec{v}}_{2} = - {|{\vec{v}}_{1}|}^{2}$
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${\vec{v}}_{1} . {\vec{v}}_{2} = - {|{\vec{v}}_{2}|}^{2}$

The following are three graphs of the magnitude of force F versus time t for a body involved in a collision.

Then the relation between the magnitude of impulse on the body in these cases is best represented by

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a > b > c
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a = b = c
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b > a > c
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c > a < b

A shell fired from a cannon explodes in mid-air. It's total

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Linear momentum is not conserved
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Linear momentum is conserved
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Kinetic energy is conserved
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Potential energy is conserved

Two bodies A and B of mass m and 2m respectively are placed on a smooth floor as shown. They are connected by a spring of constant k. If a third body C of mass m moves with a velocity $v_{0}$ along the line joining A and B and collides head-on elastically with A, then speed of A at the instant of maximum compression is

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$v_{0}$
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$\frac{v_{0}}{2}$
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$\frac{v_{0}}{4}$
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$\frac{v_{0}}{3}$

The masses $m_{1} and m_{2} (with m_{1} < m_{2})$ are connected to the two ends of a compressed spring. Now, when the masses are released on a smooth surface, they will move away with

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the same magnitude of the force.
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the equal magnitude of linear momentum.
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the greater kinetic energy of the first body than that of the second body.
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All of these

A block of mass m is attached with a spring of spring constant k as shown in the figure. Another block of mass 2m moving with speed v hits the spring. Speed of blocks at the instant of maximum compression of spring is:

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$\frac{v}{3}$
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$\frac{v}{2}$
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$\frac{2 v}{3}$
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$\frac{3 v}{2}$

A body of mass m moving with velocity v in X-direction collides with another identical body moving with the same speed in the y-direction. They coalesce into one body during a collision. The direction of motion of the composite body after the collision is

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30' with X-axis
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45° with X-axis
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60° with X-axis
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Along the y-axis

A ball strikes the floor and rebounds after an inelastic collision. Which of the following is correct?

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The total momentum of the earth and ball system is conserved.
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The total mechanical energy of the ball and earth system is conserved.
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The momentum of the ball is conserved.
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Both (1) & (2)

A sphere moving with speed u collides elastically with another identical sphere at rest. If the collision is not head-on, then the angle between their final velocities is

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0°
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60°
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90°
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45°

A ball is let to fall from a height of 32 m on the ground. The coefficient of restitution is $e = \frac{1}{2}$ . The height raised by the ball after the second rebound is

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2 m
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4 m
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8 m
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16 m

Two identical balls of mass 1 kg each moving towards each other with velocities of 3 m/s and 5 m/s respectively. The magnitude of the velocities of respective balls after the perfectly elastic head-on collision is

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3 m/s, 5 m/s
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5 m/s, 3 m/s
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4 m/s, 4 m/s
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6 m/s, 2 m/sIf the two masses are equal

Four masses are joined to light circular frames as shown in the figure. The radius of gyration of this system about an axis passing through the center of the circular frame and perpendicular to its plane would be: (where 'a' is the radius of the circle)

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$\frac{a}{\sqrt{2}}$
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$\frac{a}{2}$
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a
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2a

A disc of mass M and radius R starts falling down as shown in the figure. The string unwinds without slipping on the disc. The instantaneous power developed by the tension is:

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T x $R ω$
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$\frac{T \times R ω}{2}$
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2T x $R ω$
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Zero

When a projectile of mass 2 kg is projected from the top of a tower of height 20 m with velocity 10 m/s in the horizontal direction, then angular momentum about the lowermost point of the tower when it touches the ground is:

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600 kg $m^{2} / s$
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400 kg $m^{2} / s$
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800 kg $m^{2} / s$
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Zero

Two particles of mass 5 kg and 10 kg respectively are attached to the two ends of a rigid rod of length 1m with negligible mass. The centre of mass of the system from the 5 kg particle is nearly at a distance of :

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50 cm
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67 cm
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80 cm
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33 cm

Find the torque about the origin when a force 3 $\hat{j}$ N acts on a particle whose position vector 2 $\hat{k}$ m.

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6 $\hat{j}$ N m
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-6 $\hat{i}$ N m
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6 $\hat{k}$ N m
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6 $\hat{i}$ N m

The angular speed of the wheel of a vehicle is increased from 360 rpm to 1200 rpm in 14 seconds. Its angular acceleration is

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$~2\pi ~rad/s^{2}$
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$~28\pi ~rad/s^{2}$
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$~120\pi ~rad/s^{2}$
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$~\pi ~rad/s^{2}$

Three identical spheres, each of mass M, are placed at the corners of a right-angle triangle with mutually perpendicular sides equal to 2 m (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of the center of mass.

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$2 (\hat{i} + \hat{j})$
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$(\hat{i} + \hat{j})$
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$\frac{2}{3} (\hat{i} + \hat{j})$
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$\frac{4}{3} (\hat{i} + \hat{j})$

In the HCl molecule, the separation between the nuclei of the two atoms is about 1.27 $\overset{0}{A}$ $(1 \overset{0}{A} = 10^{- 10} m) .$ Then the approximate location of the CM of the molecule is:

(Given that a chlorine atom is about 35.5 times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus).

$(1) 1.235 \overset{0}{A} from H - atom (2) 2.41 \overset{0}{A} from Cl - atom (3) 3.40 \overset{0}{A} from Cl - atom (4) 1.07 \overset{0}{A} from H - atom$

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1
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2
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3
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4

A child sits stationary at one end of a long trolley moving uniformly with a speed V on a smooth horizontal floor. If the child gets up and runs about on the trolley in any manner, then the speed of the CM of the (trolley + child) system is:

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decreases
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increases
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remains unchanged
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none of these

A non-uniform bar of weight W is suspended at rest by two strings of negligible weight as shown in the figure. The angles made by the strings with the vertical are 36.9° and ‘ 53.1° respectively. The bar is 2 m long. The distance d of the center of gravity of the bar from its left end is:

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$(1) 69 c m (2) 72 c m (3) 73 c m (4) 74 c m$

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1
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2
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3
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4

A car weighs 1800 kg. The distance between its front and back axles is 1.8 m. Its center of gravity is 1.05 m behind the front axle. The force exerted by the level ground on each front wheel and each back wheel is respectively:

$(1) 2680 N, 5145 N (2) 5145 N, 3675 N (3) 5145 N, 5145 N (4) 3675 N, 5145 N$

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1
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2
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3
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4

Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. The angular velocity of the solid sphere is:

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more than the angular velocity of the hollow cylinder.
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less than the angular velocity of the hollow cylinder.
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equal to the angular velocity of the hollow cylinder.
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none of these.

A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s^-1. The radius of the cylinder is 0.25 m. The kinetic energy associated with the rotation of the cylinder is:

$(1) 3000 J (2) 3125 J (3) 2528 J (4) 2100 J$

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1
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2
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3
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4

A child stands at the centre of a turntable with his arms outstretched. The turntable is set to rotate with an angular speed of 40 rev/min. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to 2/5 times the initial value?

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160 rev/min
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150 rev/min
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100 rev/min
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120 rev/min

To maintain a rotor at a uniform angular speed of 200 rad s^-1, an engine needs to transmit a torque of 180 N-m. What is the power required by the engine?

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33 kW
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36 kW
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28 kW
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76 kW

A meter stick is balanced on a knife edge at its center. When two coins, each of the mass 5 gm are put one on top of the other at the 12.0 cm mark, the stick is found to be balanced at 45.0 cm. What is the mass of the meter stick?

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66 gm
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56 gm
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76 gm
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79 gm

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Practice Physics Quiz Questions and Answers

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Practice Physics Quiz Questions and Answers

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