Why are the contact points of the surface of a circular body stationary during pure rolling motion?

$A$ solid cylinder of mass $3 \, kg$ is rolling on a horizontal surface with velocity $4 \, m s^{-1}$. It collides with a horizontal spring of force constant $200 \, N m^{-1}$. The maximum compression produced in the spring will be ............... $m$.

$Assertion$: $A$ rigid disc rolls without slipping on a fixed rough horizontal surface with uniform angular velocity. Then the acceleration of the lowest point on the disc is zero.
$Reason$: For a rigid disc rolling without slipping on a fixed rough horizontal surface,the velocity of the lowest point on the disc is always zero.

$A$ wheel of a bullock cart is rolling on a level road as shown in the figure. If its linear speed is $v$ in the direction shown,which one of the following options is correct ($P$ and $Q$ are the highest and lowest points on the wheel,respectively)?

In the figure,$E$ and $v_{cm}$ represent the total energy and speed of the centre of mass of an object of mass $1 \ kg$ in pure rolling. The object is

$A$ solid disc and a ring,both of radius $10\; cm$,are placed on a horizontal table simultaneously,with an initial angular speed equal to $10\pi\; rad\; s^{-1}$. Which of the two will start to roll earlier? The coefficient of kinetic friction is $\mu_k = 0.2$.