$A$ solid cylinder $P$ rolls without slipping from rest down an inclined plane,attaining a speed $v_p$ at the bottom. Another smooth solid cylinder $Q$ of the same mass and dimensions slides without friction from rest down the inclined plane,attaining a speed $v_q$ at the bottom. The ratio of the speeds $\frac{v_q}{v_p}$ is

$A$ body starts rolling down an inclined plane of length $L$ and height $h$. This body reaches the bottom of the plane in time $t$. The relation between $L$ and $t$ is:

$A$ solid sphere,a disc,and a solid cylinder start rolling down an inclined plane from rest. All three objects are made of the same material and have the same mass. Then,

$A$ drum of radius $R$ and mass $M$ rolls down without slipping along an inclined plane of angle $\theta$. The frictional force:

When a sphere with moment of inertia $I$ rolls down an inclined plane,what percentage of its total energy is rotational kinetic energy?

$A$ cylinder of mass $10 \; kg$ and radius $15 \; cm$ is rolling perfectly on a plane of inclination $30^{\circ}$. The coefficient of static friction $\mu_{S} = 0.25$.
$(a)$ How much is the force of friction acting on the cylinder?
$(b)$ What is the work done against friction during rolling?
$(c)$ If the inclination $\theta$ of the plane is increased,at what value of $\theta$ does the cylinder begin to skid and not roll perfectly?