A wheel $A$ starts rolling up a rough inclined plane and another identical wheel $B$ starts rolling up a smooth plane having same inclination with the horizontal. If initial velocity of both the wheels is same then

A wheel $\mathrm{A}$ is connected to a second wheel $\mathrm{B}$ by means of inextensible string, passing over a pulley $\mathrm{C}$, which rotates about a fixed horizontal axle $\mathrm{O}$, as shown in the figure. The system is released from rest. The wheel $\mathrm{A}$ rolls down the inclined plane $\mathrm{OK}$ thus pulling up wheel $\mathrm{B}$ which rolls along the inclined plane $\mathrm{ON}$ Determine the velocity (in $\mathrm{m}/\mathrm{s}$ ) of the axle of wheel $\mathrm{A}$, when it has travelled a distance $s=3.5 \mathrm{m}$ down the slope. Both wheels and the pulley are assumed to be homogeneous disks of identical weight and radius. Neglect the weight of the string. The string does not slip over $\mathrm{C}$. [Take $\alpha =53°$ and $\beta =37°$ ]

Two forces of magnitude $F$ are acting on a uniform disc kept on a horizontal rough surface as shown in the figure. Friction force by the horizontal surface on the disc is $n F$. Find the value of $n$

We apply a force of $10 N$ on a cord wrapped around a cylinder of mass $2 kg$. The cylinder rolls without slipping on the floor. What is its kinetic energy (in joule) when cylinder has moved by a distance of $3/5 \mathrm{m}$.

A solid cylinder $C$ and a hollow pipe $P$ of same diameter are in contact when they are released from rest as shown in the figure on a long incline plane. Cylinder $C$ and pipe $P$ roll without slipping. Determine the clear gap (in $m$ ) between them after $2\sqrt{3}$seconds

A smooth ring of mass $m$ and radius $R=1 \mathrm{m}$ is pulled at $P$ with a constant acceleration $a=4 \mathrm{m}{ \mathrm{s}}^{-2}$ on a horizontal surface such that the plane of the ring lies on the surface. Find the angular acceleration of the ring at the given position. (in $\mathrm{rad} {\mathrm{s}}^{-2}$ )

A rolling body of mass $m=4 \mathrm{kg}$, radius $R$ and radius of gyration $k=R/\sqrt{3}$ is placed as a plank which moves with an acceleration $a=1{ \mathrm{m} \mathrm{s}}^{-2}$. Find the frictional force acting on the body if it rolls without sliding. (in $\mathrm{N}$ ).