Physics - Systems Particles Rotational Motion - Quiz-12

A hoop of radius 2 m weighs 100 kg. It rolls along a horizontal floor so that its center of mass has a speed of 20 cm/s. How much work has to be done to stop it?

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10 J
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9 J
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4 J
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6 J

The oxygen molecule has a mass of 5.30 x 10^-26 kg and a moment of inertia of 1.94 x 10^-46 kg m² about an axis through its center perpendicular to the lines joining the two atoms. Suppose the mean speed of such a molecule in a gas is 500 m/s and that its kinetic energy of rotation is two-thirds of its kinetic energy of translation. Find the average angular velocity of the molecule.

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$5.7 \times 10^{11} r a d s^{- 1}$
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$5.7 \times 10^{12} r a d s^{- 1}$
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$6.7 \times 10^{11} r a d s^{- 1}$
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$6.7 \times 10^{12} r a d s^{- 1}$

A solid cylinder rolls up an inclined plane of the angle of inclination 30°. At the bottom of the inclined plane, the centre of mass of the cylinder has a speed of 5 m/s. How far will the cylinder go up the plane?

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4.9 m
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1.3 m
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4.7 m
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3.8 m

A man stands on a rotating platform, with his arms stretched horizontally holding a 5 kg weight in each hand. The angular speed of the platform is 30 revolutions per minute. The man then brings his arms close to his body with the distance of each weight from the axis changing from 90 cm to 20 cm. The moment of inertia of the man together with the platform may be taken to be constant and equal to 7.6 kg m². What is his new angular speed?

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60 rev/min
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57.0 rev/min
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58.8 rev/min
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60.1 rev/min

Two like parallel forces 20 N and 30 N act at the ends A and B of a rod 1.5 m long. The resultant of the forces will act at the point

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90 cm from A
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75 cm from B
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20 cm from B
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85 cm from A

A bullet of mass 10 g and speed 500 m/s is fired into a door and gets embedded exactly at the center of the door. The door is 1.0 m wide and weighs 12 kg. It is hinged at one end and rotates about a vertical axis practically without friction. The angular speed of the door just after the bullet embeds into it is:

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0.122 rad/s
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0.625 rad/s
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0.231 rad/s
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0.191 rad/s

A disc rotating about its axis with angular speed $ω_{0}$ is placed lightly (without any translational push) on a perfectly frictionless table. The radius of the disc is R. The linear velocities of the points A, B, and C on the disc (as shown in the figure) respectively are:

$(1) ω_{0} R, ω_{0} R, \frac{ω_{0} R}{2} (2) \frac{ω_{0} R}{2}, ω_{0} R, ω_{0} R (3) ω_{0} R, \frac{ω_{0} R}{2}, ω_{0} R (4) ω_{0} R, ω_{0} R, 0$

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1
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2
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3
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4

A cylinder of mass 10 kg and radius of 15 cm is rolling perfectly on a plane of inclination 30°. The coefficient of static friction $μ_{s}$ = 0.25. How much is the force of friction acting on the cylinder?

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(3) 19.1 N
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(2) 15.5 N
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(1) 16.3 N
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(4) 20.0 N

A U-238 nucleus originally at rest, decays by emitting an $α$ -particle, say with a velocity of v m/s. The recoil velocity (in ms^-1) of the residual nucleus is

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$\frac{4 v}{238}$
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$- \frac{4 v}{238}$
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$\frac{v}{4}$
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$- \frac{4 v}{234}$

An object of mass 80 kg moving with velocity 2 ms^-1 hit by collides with another object of mass 20 kg moving with velocity 4 ms^-1. Find the loss of energy assuming a perfectly inelastic collision

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12 J
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24 J
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30 J
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32 J

Particle A makes a perfectly elastic collision with another particle B at rest. They fly apart in opposite directions with equal speeds. If their masses are m_A and m_B respectively, then

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2m_A = m_B
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3m_A = m_B
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4m_A = m_B
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$\sqrt{3}$ m_A = m_B

A body of mass 10 kg moving with speed of 3 ms^-1 collides with another stationary body of mass 5 kg. As a result, the two bodies stick together. The KE of composite mass will be

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30 J
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60 J
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90 J
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120 J

Select the false statement

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In elastic collision, KE is not conserved during the collision
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The coefficient of restitution for a collision between two steel balls lies between 0 and 1
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The momentum of a ball colliding elastically with the floor is conserved
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In an oblique elastic collision between two identical bodies with one of them at rest initially, the final velocities are perpendicular

A bullet of mass m moving with a velocity u strikes a block of mass M at rest and gets embedded in the block. The loss of kinetic energy in the impact is

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$\frac{1}{2} {mMu}^{2}$
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$\frac{1}{2} (m + M) u^{2}$
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$\frac{{mMu}^{2}}{2 (m + M)}$
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$(\frac{m + M}{2 mM}) u^{2}$

A bullet of mass m moving with velocity v strikes a suspended wooden block of mass M. If the block rises to height h, the initial velocity of the bullet will be

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$\sqrt{2 gh}$
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$\frac{M + m}{m} \sqrt{2 gh}$
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$\frac{m}{M + m} \sqrt{2 gh}$
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$\frac{M + m}{M} \sqrt{2 gh}$

A ball is allowed to fall from a height of 10 m. If there is 40% loss of energy due to impact, then after one impact ball will go up by

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10 m
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8 m
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4 m
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6 m

A ball of mass M moving with speed v collides perfectly inelastically with another ball of mass m at rest. The magnitude of impulse imparted to the first ball is

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Mv
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mv
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$\frac{Mm}{M + m} v$
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$\frac{M^{2}}{M + m} v$

A man of mass m starts moving on a plank of mass M with constant velocity v with respect to plank. If the plank lles on a smooth horizontal surface, then velocity of plank with respect to ground is

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$\frac{M v}{m + M}$
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$\frac{m v}{M}$
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$\frac{M v}{m}$
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$\frac{m v}{m + M}$

A ball of mass m is thrown upward and another ball of same mass is thrown downward so as to move freely under gravity. The acceleration of centre of mass is

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g
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$\frac{g}{2}$
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2g
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Zero

A hollow sphere of mass 1 kg and radius 10 cm is free to rotate about its diameter. If a force of 30 N is applied tangentially to it, its angular acceleration is (in rad/s²)

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5000
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450
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50
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5

Two equal and opposite forces are applied tangentially to a uniform disc of mass M and radius R as shown in the figure. If the disc is pivoted at its centre and free to rotate in its plane, the angular acceleration of the disc is

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$\frac{F}{M R}$
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$\frac{2 F}{3 M R}$
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$\frac{4 F}{M R}$
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Zero

A wheel having moment of inertia 4 kg m² about its symmetrical axis, rotates at rate of 240 rpm about it. The torque which can stop the rotation of the wheel in one minute is

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$\frac{5 π}{7} Nm$
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$\frac{8 π}{15} Nm$
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$\frac{2 π}{9} Nm$
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$\frac{3 π}{7} Nm$

A force $\vec{F} = (2 \hat{i} + 3 \hat{j} - 5 \hat{k}) N$ acts at a point ${\vec{r}}_{1} = (2 \hat{i} + 4 \hat{j} + 7 \hat{k}) m .$ The torque of the force about the point ${\vec{r}}_{2} = (\hat{i} + 2 \hat{j} + 3 \hat{k}) m$ is

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$(17 \hat{j} + 5 \hat{k} - 3 \hat{i}) Nm$
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$(2 \hat{i} + 4 \hat{j} - 6 \hat{k}) Nm$
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$(12 \hat{i} - 5 \hat{j} + 7 \hat{k}) Nm$
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$(-22 i+13 \hat{j} - \hat{k}) Nm$

A particle of mass 5 kg is moving with a uniform speed 3 $\sqrt{2}$ in XOY plane along the line Y = X + 4. The magnitude of its angular momentum about the origin is

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40 units
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60 units
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Zero
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40 $\sqrt{2}$ units

The moment of inertia of a body depends on

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The mass of the body
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The distribution of the mass in the body
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The axis of rotation of the body
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All of these

The two spheres, one of which is hollow and other solid, have identical masses and moment of inertia about their respective diameters. The ratio of their radi is given by

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5 : 7
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3 : 5
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$\sqrt{3} : \sqrt{5}$
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3 : 7

A meter stick is held vertically with one end on the floor and is allowed to fall. The speed of the other end when it hits the floor assuming that the end at the floor does not slip is (g=9.8 m/s²)

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3.2 m/s
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5.4 m/s
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7.6 m/s
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9.2 m/s

A circular disc of mass 2 kg and radius 10 cm rolls without slipping with a speed 2 m/s. The total kinetic energy of disc is

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10 J
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6 J
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2 J
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4 J

A horizontal disc rotating freely about a vertical axis through its centre makes 90 revolutions per minute. A small piece of wax of mass m falls vertically on the disc and sticks to it at a distance r from the axis. If the number of revolutions per minute reduce to 60 , then the moment of inertia of the disc is

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mr²
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$\frac{3}{2} m r^{2}$
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2 mr²
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3 mr²

The angular momentum of a particle performing uniform circular motion is L. If the kinetic energy of partical is doubled and frequency is halved, then angular momentum becomes

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$\frac{L}{2}$
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2L
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$\frac{L}{4}$
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4L

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Practice Physics Quiz Questions and Answers

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Practice Physics Quiz Questions and Answers

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