# NCERT Class 11 Physics Solutions: Chapter 7 – System of Particles and Rotation Motion-Part 14 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 7.31:

A cylinder of mass and radius is rolling perfectly on a plane of inclination The coefficient of static friction .

(a) How much is the force of friction acting on the cylinder?

(b) What is the work done against friction during rolling?

(c) If the inclination of the plane is increased, at what value of does the cylinder begin to skid, and not roll perfectly?

Mass of the cylinder,

Co-efficient of kinetic friction,

Angle of inclination,

Moment of inertia of a solid cylinder about its geometric axis,

The various forces acting on the cylinder are shown in the following figure: The Various Forces Acting on the Cylinder Are Shown in the F …

The acceleration of the cylinder is given as:

The force of friction acting on the cylinder:

Using Newton՚s second law of motion, we can write net force as:

The work done against friction during rolling:

During rolling, the instantaneous point of contact with the plane comes to rest. Hence, the work done against frictional force is zero.

For rolling without skid, we have the relation:

Question 7.32:

Read each statement below carefully, and state, with reasons, if it is true or false;

(a) During rolling, the force of friction acts in the same direction as the direction of motion of the CM of the body.

(b) The instantaneous speed of the point of contact during rolling is zero.

(c) The instantaneous acceleration of the point of contact during rolling is zero.

(d) For perfect rolling motion, work done against friction is zero.

(e) A wheel moving down a perfectly frictionless inclined plane will undergo slipping (not rolling) motion.

False

Explanation:

Frictional force acts opposite to the direction of motion of the centre of mass of a body. In the case of rolling, the direction of motion of the centre of mass is backward. Hence, frictional force acts in the forward direction.

True

Explanation:

Rolling can be considered as the rotation of a body about an axis passing through the point of contact of the body with the ground. Hence, its instantaneous speed is zero.

False

Explanation:

When a body is rolling, its instantaneous acceleration is not equal to zero. It has some value.

True

Explanation:

When perfect rolling begins, the frictional force acting at the lowermost point becomes zero. Hence, the work done against friction is also zero.

True

Explanation:

The rolling of a body occurs when a frictional force acts between the body and the surface. This frictional force provides the torque necessary for rolling. In the absence of a frictional force, the body slips from the inclined plane under the effect of its own weight.

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