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A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down(no rolling) the plane. Then maximum acceleration down the plane is for

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Important Questions on Motion of System of Particles and Rigid Body

MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

Consider a cylinder of mass M resting on a rough horizontal rug that is pulled out from under it with acceleration 'a' perpendicular to the axis of the cylinder. What is F_friction at point P ? It is assumed that the cylinder does not slip.
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MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

A solid sphere rolls without slipping, first horizontally and then up to a point $x$ at height $h$ on an inclined plane before rolling down, as shown in the figure below.

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The initial horizontal speed of the sphere is

EASY

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

A solid sphere of mass

2 kg

is rolling on a frictionless horizontal surface with velocity

6 m s^{- 1}

. It collides on the free end of an ideal spring whose other end is fixed. The maximum compression produced in the spring will be (Force constant of the spring =

36 N m^{- 1}

MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

A uniform sphere of mass

500 g

rolls without slipping on a plane horizontal surface with its centre moving at a speed of

5.00 cm s^{- 1}

. Its kinetic energy is:

HARD

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

On a pulley of mass $M$ hangs a rope with two masses $m_{1}$ and $m_{2} (m_{1} > m_{2})$ tied at the ends as shown in the figure. The pulley rotates without any friction, whereas the friction between the rope and the pulley is large enough to prevent any slipping. Which of the following plots best represents the difference between the tensions in the rope on the two sides of the pulley as a function of the mass of the pulley?

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EASY

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

A disc of radius

2 m

and mass

100 k g

rolls on a horizontal floor. Its centre of mass has speed of

20 c m s^{- 1} .

How much work is needed to stop it?

HARD

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

A uniform solid cylindrical roller of mass

m

is being pulled on a horizontal surface with force

F

parallel to the surface and applied at its centre. If the acceleration of the cylinder is

a

and it is rolling without slipping then the value of

F

is:

MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

A sphere rolls down an inclined plane of inclination

θ

. What is the acceleration as the sphere reaches bottom?

HARD

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

V -

shaped rigid body has two identical uniform arms. What must be the angle between the two arms, so that when the body is hung from one end the other arm is horizontal?

MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

A rigid ball rolls without slipping on a surface shown below.

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Which on the following is the most likely representation of the distance travelled by the ball vs time graph?

MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

A wheel is rotating freely with an angular speed

ω

on a shaft. The moment of inertia of the wheel is

I

and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia

3 I

initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is:

MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

Consider two uniform discs of the same thickness and different radii

R_{1} = R

and

R_{2} = α R

made of the same material. If the ratio of their moments of inertia

I_{1}

and

I_{2}

, respectively, about their axes is

I_{1} : I_{2} = 1 : 16

then the value of

α

is :

HARD

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

A small roller of diameter $20 cm$ has an axle of diameter $10 cm$ (see figure below on the left). It is on a horizontal floor and a meter scale is positioned horizontally on its axle with one edge of the scale on top of the axle (see figure on the right). The scale is now pushed slowly on the axle so that it moves without slipping on the axle, and the roller starts rolling without slipping. After the roller has moved $50 cm,$ the position of the scale will look like (figures are schematic and not drawn to scale)

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MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CD which are placed asymmetrically (see figure), with its axis perpendicular to CD and its centre O at the centre of line joining AB and CD (see figure). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to:

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EASY

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

A solid cylinder of mass

M

and radius

R

rolls down a smooth inclined plane about its own axis and reaches the bottom with velocity

v

. The height of the inclined plane is (

g =

acceleration due to gravity)

HARD

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

A sphere of radius $a$ and mass $m$ rolls along a horizontal plane with constant speed $v_{0}$ . It encounters an inclined plane at angle $θ$ and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel?

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EASY

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

In a bicycle, the radius of rear wheel is twice the radius of front wheel. If

r_{f}

and

r_{r}

are the radius,

v_{f}

and

v_{r}

are the speeds of top most points of wheel, then

HARD

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

A solid cylinder P rolls without slipping from rest down an inclined plane attaining a speed

v_{P}

at the bottom. Another smooth solid cylinder

Q

of same mass and dimensions slides without friction from rest down the inclined plane attaining a speed

v_{Q}

at the bottom. The ratio of the speeds

(\frac{v_{Q}}{v_{P}})

is -

MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

A wheel of radius "rolls without slipping with a speed $v$ on a horizontal road. When it is at a point $A$ on the road a small bob of the mud separates from wheel at the highest point and touches the point $B$ on the road as shown in the figure. Then $A B$ is (g-acceleration due to gravity)

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MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Body>Translation and Rotation of a Body

A rigid massless rod of length $3 l$ has two masses attached at each end as shown in the figure. The rod is pivoted at point $P$ on the horizontal axis. When released from the initial horizontal position, its instantaneous angular acceleration will be

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A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down(no rolling) the plane. Then maximum acceleration down the plane is for

Important Questions on Motion of System of Particles and Rigid Body

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