Question

The motion of a sphere moving on a rough horizontal surface changes from pure sliding (without rolling) to pure rolling (without slipping). In this process, the force of friction:

• A. initially acts opposite to the direction of motion and later in the direction of motion
• B. causes linear retardation
• C. causes angular acceleration
• D. stops acting when pure rolling begins

Answer 1

Answer: (B), (C), (D)

The correct options are
B causes linear retardation
C causes angular acceleration
D stops acting when pure rolling begins

As the point A tends to slide forwards, thus kinetic friction force acts in backward direction i.e opposite to the direction of motion.

Hence it causes linear retardation. $a=\frac{-f}{m}$

Also friction force provides the torque required for the body to do rotational motion, thus it causes angular acceleration.

$\tau =I\alpha$

$fR=I\alpha ⟹\alpha =\frac{fR}{I}$

Also when pure rolling will start, then the point A will no longer slide on the surface. Thus there is no need of friction at that time, hence it will cease.