Consider a point $P$ on the circumference of a disc rolling along a horizontal surface. If $R$ is the radius of the disc,the distance through which $P$ moves in one full rotation of the disc is:

$A$ circular disc rolls on a horizontal floor without slipping and the centre of the disc moves with a uniform velocity $v$. Which of the following values can the velocity of a point on the rim of the disc have?

$A$ uniform solid cylinder of mass $M = 3 \ kg$ and radius $R = 10 \ cm$ is connected about an axis through the centre of the cylinder to a horizontal spring with spring constant $k = 8 \ N/m$. The cylinder is pulled back,stretching the spring $x = 1 \ m$ from equilibrium. When released,the cylinder rolls without slipping. What is the speed of the center of the cylinder when it returns to equilibrium? .................. $m/s$

$A$ circular disc of mass $0.41 \ kg$ and radius $10 \ m$ rolls without slipping with a velocity of $2 \ m/s$. The total kinetic energy of the disc is ....... $J$.

$A$ uniform solid cylinder of mass $m$ and radius $R$ is set in rotation about its axis with an angular velocity $\omega_0$,then lowered with its lateral surface onto a horizontal plane and released. The coefficient of friction between the cylinder and plane is equal to $\mu$. The time after which the cylinder starts rolling without slipping is

$A$ solid sphere of mass $2 \ kg$ is rolling on a frictionless horizontal surface with velocity $6 \ m \ s^{-1}$. It collides with the free end of an ideal spring whose other end is fixed. The maximum compression produced in the spring will be (Force constant of the spring $= 36 \ N \ m^{-1}$). (in $m$)