Pure Rolling

If a thin ring is subjected to a force $F$ as shown in the figure. Find the force of friction required to make sure that the ring does pure rolling on the rough surface.
 

A car starts from rest to cover a distance $s$. The coefficient of friction between the road and the tyres is $\mu$. The minimum time in which the car covers the distance is proportional to

A uniform solid ball of mass '$m$' rolls without sliding on a fixed horizontal surface. The velocity of the lowest point of the ball with respect to the center of the ball is $v$. The total kinetic energy of the ball is:

A ring of radius $3a$ is fixed rigidly on a table. A small ring whose mass is $m$ and radius $a$ rolls without slipping inside it as shown in the figure. The small ring is released from position $A$. When it reaches the lowest point, the speed of the centre of the ring at that time would be,

A small sphere rolls down without slipping from the top of a track in a vertical plane as shown. The track has an elevated section and a horizontal path. The horizontal part is $1.0 \mathrm{m}$ above the ground level and the top of the track is $2.4 \mathrm{m}$ above the ground. Find the distance on the ground with respect to a point $B$ where the sphere lands.

A solid sphere is rolling on a frictionless surface, as shown in figure with a translational velocity $v \mathrm{m} {\mathrm{s}}^{-1}$. If it has to climb the inclined surface, then $v$ should be

In the previous, which of the bodies reaches the ground with maximum rotational kinetic energy?

What is the work done against friction during rolling, if length of the incline is $1$ meter?

A ring of mass $m$ and radius $R$ is acted upon by a force $F$ as shown in the figure. There is sufficient friction between the ring and the ground. The force of friction necessary for pure rolling is

A hollow smooth uniform sphere A of mass $\text{'}m\text{'}$ rolls without sliding on a smooth horizontal surface. It collides elastically and head on with another stationary smooth solid sphere $B$ of the same mass $m$ and same radius. The ratio of kinetic energy of $\text{'}B\text{'}$ to that of $\text{'}A\text{'}$ just after the collision is :

A uniform solid sphere of radius $r$ is released on a rough horizontal floor after imparting it an initial horizontal velocity vo and angular velocity ${\omega }_0$ as shown in the figure below. Coefficient of friction between sphere and ground is $\mu .$ What should be the relation between vo and $\omega 0$ so that the sphere comes to permanent rest after sometime?

A uniform solid sphere is released from the top point of an incline plane. If the incline surface is smooth the sphere takes a time $t_1$ to slide down. If the surface of incline is sufficient rough so that the sphere can roll without sliding the sphere takes time $t_2$ to roll down the same incline, $\frac{t_1}{t_2}$ will be :

In rotational motion of a rigid body, all particles move with _____.

A solid cylinder rolls without slipping down an inclined plane at an angle $60°$ with the horizontal. The acceleration of the cylinder is

A rolling body was initially at rest on a rough floor and a force $F$ (parallel to floor) is applied on the top of the rolling body. Choose the correct option for the pure accelerated rolling.

A wheel is rolling straight on the ground without slipping. If the axis of the wheel has speed $v$, the instantaneous velocity of a point $P$ on the rim, defined by angle $\mathrm{\theta }$, relative to the ground will be :

A circular disc is rolling on a horizontal plane. Its total kinetic energy is $300 \mathrm{J}.$What is its translational $\mathrm{K}.\mathrm{E}.$

The total work done by frictional force in pure rolling is always

A thin uniform circular ring first slips down a smooth inclined plane. In second case, it rolls down through a rough inclined plane of identical geometry from same height. The ratio of time taken in the two cases is (assume in both case ring is released from rest)

A ring of mass $\mathrm{m}=1\mathrm{kg}$ and radius $\mathrm{R}=1.25 \mathrm{m}$ is kept on a rough horizontal ground. A small body of same mass $\mathrm{m}=1\mathrm{kg}$ is struck to the top of the ring. When it was given a slight push forward, the ring started rolling purely on the ground. What is the maximum speed of the centre of the ring (in $\mathrm{m} {\mathrm{s}}^{-1}$)