$A$ 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 $g=10\,ms^{-2}$)

$A$ solid sphere of mass $4 \ kg$ and radius $28 \ cm$ is on an inclined plane. If the acceleration of the sphere when it rolls down without sliding is $3.5 \ m \ s^{-2}$,then the acceleration of the sphere when it slides down without rolling is (in $m \ s^{-2}$)

$A$ solid cylinder of mass $m$ and radius $R$ rolls down an inclined plane of height $30 \ m$ without slipping. The speed of its centre of mass when the cylinder reaches the bottom is $[$use $g=10 \ m \ s^{-2}]$ (in $m \ s^{-1}$)

$A$ disc of radius $R$ and mass $M$ is rolling horizontally without slipping with speed $v$. It then moves up an inclined smooth surface as shown in figure. The maximum height that the disc can go up the incline is:

$A$ 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 spherical ball is rolled up an inclined plane of angle of inclination $30^{\circ}$ with an initial speed of $4 \ m/s$ at the bottom of the inclination. How far will the ball go up the plane (in $cm$)? (Use $g=10 \ m/s^2$)