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A thin plank of mass $m$ is kept on two rollers such that the centre of mass of the plank is midway between the points of contact with the rollers. Friction is sufficient everywhere to prevent slipping. A force $F$ whose magnitude can be varied is applied parallel to the plank as shown in the figure.

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Important Questions on Motion of System of Particles and Rigid Body

EASY

Physics>Mechanics>Motion of System of Particles and Rigid Body>Centre of Mass

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>Motion of System of Particles and Rigid Body>Centre of Mass

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>Motion of System of Particles and Rigid Body>Centre of Mass

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>Motion of System of Particles and Rigid Body>Centre of Mass

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>Motion of System of Particles and Rigid Body>Centre of Mass

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>Motion of System of Particles and Rigid Body>Centre of Mass

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>Motion of System of Particles and Rigid Body>Centre of Mass

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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MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Body>Centre of Mass

The position vector of the center of mass

{\vec{r}}_{cm}

of an asymmetric uniform bar of negligible area of cross-section as shown in figure is:

Question Image

MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Body>Centre of Mass

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>Motion of System of Particles and Rigid Body>Centre of Mass

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>Motion of System of Particles and Rigid Body>Centre of Mass

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>Motion of System of Particles and Rigid Body>Centre of Mass

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>Motion of System of Particles and Rigid Body>Centre of Mass

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>Motion of System of Particles and Rigid Body>Centre of Mass

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>Motion of System of Particles and Rigid Body>Centre of Mass

Distance of the centre of mass of a solid uniform cone from its vertex is

z_{0}

. If the radius of its base is

R

and its height is

h

then

z_{0}

is equal to:

EASY

Physics>Mechanics>Motion of System of Particles and Rigid Body>Centre of Mass

Two spherical bodies of mass M and 5M and radii R and 2R released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is:

MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Body>Centre of Mass

A uniform thin rod AB of length

L

has linear mass density

μ (x) = a + \frac{b x}{L}

, where

x

is measured from A. If the CM of the rod lies at a distance of

(\frac{7}{12} L)

from A, then

a

and

b

are related as:

MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Body>Centre of Mass

A sphere rolls down an inclined plane of inclination

θ

. What is the acceleration as the sphere reaches bottom?

MEDIUM

Physics>Mechanics>Motion of System of Particles and Rigid Body>Centre of Mass

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>Motion of System of Particles and Rigid Body>Centre of Mass

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 thin plank of mass m is kept on two rollers such that the centre of mass of the plank is midway between the points of contact with the rollers. Friction is sufficient everywhere to prevent slipping. A force F whose magnitude can be varied is applied parallel to the plank as shown in the figure.

Important Questions on Motion of System of Particles and Rigid Body

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