$A$ disc of radius $R$ is rolling down an inclined plane whose angle of inclination is $\theta$. Its acceleration would be

$A$ circular disc reaches from top to bottom of an inclined plane of length $l$. When it slips down the plane,it takes $t \ s$. When it rolls down the plane,it takes $\left(\frac{\alpha}{2}\right)^{1/2} t \ s$,where $\alpha$ is:

$A$ hollow cylinder is rolling on an inclined plane,inclined at an angle of $30^{\circ}$ to the horizontal. Its speed after travelling a distance of $10 \ m$ will be .......... $m/s$.

$A$ solid sphere is rolling down an inclined plane. What is the ratio of its translational kinetic energy to its rotational kinetic energy?

$A$ cylinder and a ring of same mass $M$ and radius $R$ are placed on the top of a rough inclined plane of inclination $\theta$. Both are released simultaneously from the same height $h$. When these bodies roll down to the foot of the inclined plane,then

$A$ rolling wheel of $12 \, kg$ is on an inclined plane at position $P$ and connected to a mass of $3 \, kg$ through a string of fixed length and a pulley as shown in the figure. Consider $PR$ as a friction-free surface. The velocity of the centre of mass of the wheel when it reaches the bottom $Q$ of the inclined plane $PQ$ will be $\frac{1}{2} \sqrt{xgh} \, m/s$. The value of $x$ is.............