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A solid sphere is in pure rolling motion on an inclined surface having inclination θ

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Important Questions on Rotational Mechanics

EASY

Physics>Mechanics>Rotational Mechanics>Pure Rolling

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?

MEDIUM

Physics>Mechanics>Rotational Mechanics>Pure Rolling

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:

HARD

Physics>Mechanics>Rotational Mechanics>Pure Rolling

A circular disc reaches from top to bottom of an inclined plane of length

L .

When it slips down the plane, it takes time

t_{1}

. When it rolls down the plane, it takes time

t_{2}

. The value of

\frac{t_{2}}{t_{1}}

\sqrt{\frac{3}{x}}

. The value of

x

will be

HARD

Physics>Mechanics>Rotational Mechanics>Pure Rolling

A horizontal force $F$ is applied at the centre of mass of a cylindrical object of mass $m$ and radius $R$ , perpendicular to its axis as shown in the figure. The coefficient of friction between the object and the ground is $μ$ . The centre of mass of the object has an acceleration $a$ . The acceleration due to gravity is $g$ . Given that the object rolls without slipping, which of the following statement(s) is (are) correct?

Question Image

HARD

Physics>Mechanics>Rotational Mechanics>Pure Rolling

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}

MEDIUM

Physics>Mechanics>Rotational Mechanics>Pure Rolling

A solid cylinder of mass

' m'

and radius

' r'

starts rolling down an inclined plane of inclination

θ .

If the friction is just enough to prevent slipping. the speed of its centre of mass after it has descended through a height

' h'

is given by

HARD

Physics>Mechanics>Rotational Mechanics>Pure Rolling

A sphere of mass $2 kg$ and radius $0.5 m$ is rolling with an initial speed of $1 {m s}^{- 1}$ goes up an inclined plane which makes an angle of $30 °$ with the horizontal plane, without slipping. How low will the sphere take to return to the starting point $A$ ?

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HARD

Physics>Mechanics>Rotational Mechanics>Pure Rolling

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

MEDIUM

Physics>Mechanics>Rotational Mechanics>Pure Rolling

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

EASY

Physics>Mechanics>Rotational Mechanics>Pure Rolling

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

EASY

Physics>Mechanics>Rotational Mechanics>Pure Rolling

A car starts from rest to cover a distance

s

. The coefficient of friction between the road and the tyres is

μ

. The minimum time in which the car covers the distance is proportional to

MEDIUM

Physics>Mechanics>Rotational Mechanics>Pure Rolling

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

Physics>Mechanics>Rotational Mechanics>Pure Rolling

A solid cylinder of mass

m

and radius

R

rolls down an inclined plane of height

30 m

without slipping. The speed of its centre of mass when the cylinder reaches the bottom is [use

g = 10 m s^{- 2}

]

MEDIUM

Physics>Mechanics>Rotational Mechanics>Pure Rolling

Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter. The correct statement for this situation is

HARD

Physics>Mechanics>Rotational Mechanics>Pure Rolling

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>Rotational Mechanics>Pure Rolling

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

Physics>Mechanics>Rotational Mechanics>Pure Rolling

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.
Question Image

MEDIUM

Physics>Mechanics>Rotational Mechanics>Pure Rolling

A sphere rolls down an inclined plane of inclination

θ

. What is the acceleration as the sphere reaches bottom?

MEDIUM

Physics>Mechanics>Rotational Mechanics>Pure Rolling

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:

HARD

Physics>Mechanics>Rotational Mechanics>Pure Rolling

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 :

A solid sphere is in pure rolling motion on an inclined surface having inclination θ

Important Questions on Rotational Mechanics

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