An object is rolling on an inclined plane. Its linear and rotational kinetic energies are equal. The object is:

$A$ ball is rolling without slipping. The radius of gyration of the ball about an axis passing through its center of mass is $K$. If the radius of the ball is $R$,what fraction of the total energy is rotational kinetic energy?

$A$ round uniform body of radius $R$,mass $M$,and moment of inertia $I$ rolls down (without slipping) an inclined plane making an angle $\theta$ with the horizontal. Then its acceleration is

$A$ solid cylinder is suspended symmetrically by two massless strings,as shown in the figure. The distance the cylinder should fall by unbinding the strings to achieve a speed of $4\,ms^{-1}$ is $........cm$. (Take $g=10\,ms^{-2}$)

$A$ 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?

$A$ spherical uniform body of radius $R$,mass $M$,and moment of inertia $I$ rolls down (without slipping) on an inclined plane making an angle $\theta$ with the horizontal. Then its acceleration is