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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)

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Important Questions on Motion of System of Particles

MEDIUM

General Science>Physics>Motion of System of Particles>Rolling Motion

The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane: (i) a ring of radius

R,

(ii) a solid cylinder of radius

\frac{R}{2}

and (iii) a solid sphere of radius

\frac{R}{4} .

If, in each case, the speed of the center of mass at the bottom of the incline is same, the ratio of the maximum heights they climb is:

MEDIUM

General Science>Physics>Motion of System of Particles>Rolling Motion

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:

Question Image

MEDIUM

General Science>Physics>Motion of System of Particles>Rolling Motion

The ratio of the acceleration for a solid sphere (mass

‘ m'

and radius

R)

rolling down an incline of angle

‘ θ'

without slipping and slipping down the incline without rolling is:

MEDIUM

General Science>Physics>Motion of System of Particles>Rolling Motion

A solid cylinder of mass $m$ and radius $R$ rolls down inclined plane without slipping. The speed of its $C . M .$ when it reaches the bottom is___

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HARD

General Science>Physics>Motion of System of Particles>Rolling Motion

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:

HARD

General Science>Physics>Motion of System of Particles>Rolling Motion

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

General Science>Physics>Motion of System of Particles>Rolling Motion

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights $h_{s p h}$ and $h_{c y l}$ on the incline. The ratio $\frac{h_{s p h}}{h_{c y l}}$ is given by:
Question Image

EASY

General Science>Physics>Motion of System of Particles>Rolling Motion

A solid sphere of radius

R

makes a perfect rolling down on a plane which is inclined to the horizontal axis at an angle

θ

. If the radius of gyration is

k

, then its acceleration is

HARD

General Science>Physics>Motion of System of Particles>Rolling Motion

A uniform thin rod of length

2 L

and mass

m

lies on a horizontal table. A horizontal impulse

J

is given to the rod at one end. There is no friction. The total kinetic energy of the rod just after the impulse will be

HARD

General Science>Physics>Motion of System of Particles>Rolling Motion

A cylinder of mass M_c and sphere of mass M_s are placed at points A and B of two inclines, respectively. (See figure). If they roll on the incline without slipping such that their accelerations are the same, then the ratio

\frac{sin θ_{c}}{sin θ_{s}}

is :

MEDIUM

General Science>Physics>Motion of System of Particles>Rolling Motion

A uniform solid cylindrical roller of mass

m

is being pulled on horizontal surface with force

F

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

a

and it is rolling without slipping, then the value of

F

MEDIUM

General Science>Physics>Motion of System of Particles>Rolling Motion

A homogeneous solid cylindrical roller of radius

R

and mass

M

is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is:

MEDIUM

General Science>Physics>Motion of System of Particles>Rolling Motion

A cylinder of mass

2 kg

is released from rest from the top of an inclined plane of inclination

30 °

and length

1 m

. If the cylinder rolls without slipping, then its speed when it reaches the bottom is [

g = 10 m s^{- 2}

]

MEDIUM

General Science>Physics>Motion of System of Particles>Rolling Motion

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:

MEDIUM

General Science>Physics>Motion of System of Particles>Rolling Motion

A disc of mass

M

and radius

R

rolls without slipping on a level surface with a linear speed

v

. Its kinetic energy will be given by

MEDIUM

General Science>Physics>Motion of System of Particles>Rolling Motion

A sphere rolls down an inclined plane of inclination

θ

. What is the acceleration as the sphere reaches bottom?

EASY

General Science>Physics>Motion of System of Particles>Rolling Motion

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

MEDIUM

General Science>Physics>Motion of System of Particles>Rolling Motion

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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HARD

General Science>Physics>Motion of System of Particles>Rolling Motion

A ring and a disc are initially at rest, side by side, at the top of an inclined plane which makes an angle

60 °

with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground is

\frac{(2 - \sqrt{3})}{\sqrt{10}} s

, then the height of the top of the inclined plane (in meters) is __________. Take

g = 10 m s^{- 2}

EASY

General Science>Physics>Motion of System of Particles>Rolling Motion

A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

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)

Important Questions on Motion of System of Particles

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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)