$A$ disc is performing pure rolling on a smooth stationary surface with constant angular velocity as shown in the figure. At any instant,for the lowermost point of the disc -

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 the friction force $F_{friction}$ at point $P$? It is assumed that the cylinder does not slip.

$A$ body is rolling without slipping on a horizontal plane. If the rotational kinetic energy of the body is $40\%$ of the total kinetic energy,then the body might be:

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.

$A$ force of $49 \ N$ acts tangentially at the highest point of a solid sphere of mass $20 \ kg$,kept on a rough horizontal plane. If the sphere rolls without slipping,then the acceleration of the center of the sphere is (in $m/s^2$)

$A$ sphere of mass $50\,g$ and diameter $20\,cm$ rolls without slipping with a velocity of $5\,cm/s$. Its total kinetic energy is