A solid uniform disc of mass $m$ rolls without slipping down a fixed inclined plank with an acceleration $a$. The frictional force on the disc due to the surface of the plane is

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

A smooth inclined plane fixed in a car accelerating on a horizontal road is shown in figure. The angle of incline $\theta$ is related to the acceleration a of the car as $a=g\tan \theta$. If the sphere is set in pure rolling on the incline

A disc of mass $M$ and radius $R$ is rolling with angular speed $\omega$ on a horizontal plane as shown. The magnitude of angular momentum of the disc about the origin $\mathrm{O}$ is 

A cubical block of side $L$ rests on a rough horizontal surface with coefficient of friction $\mu .$ A horizontal force $F$ is applied on the block as shown If the coefficient of friction is sufficiently high so that the block does not slide before toppling, the minimum force required to topple the block is