$A$ cylinder of mass $m$ and radius $R$ rolls without slipping down an inclined plane of length $L$ and height $h$. What will be the velocity of its center of mass when the cylinder reaches the bottom?

$A$ uniform solid sphere of mass $m$ and radius $r$ rolls without slipping down an inclined plane,inclined at an angle $45^o$ to the horizontal. Find the minimum magnitude of the frictional coefficient required for rolling without slipping.

$A$ solid cylinder rolls up an inclined plane of angle of inclination $30^{\circ}$. At the bottom of the inclined plane,the centre of mass of the cylinder has a speed of $5 \; m/s$.
$(a)$ How far will the cylinder go up the plane?
$(b)$ How long will it take to return to the bottom?

$A$ circular disc reaches from top to bottom of an inclined plane of length $L$. When it slips down the plane,it takes time $t_{1}$. When it rolls down the plane,it takes time $t_{2}$. The value of $\frac{t_{2}}{t_{1}}$ is $\sqrt{\frac{3}{x}}$. The value of $x$ will be .... .

Two solid cylinders $P$ and $Q$ of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder $P$ has most of its mass concentrated near its surface,while $Q$ has most of its mass concentrated near the axis. Which statement$(s)$ is (are) correct?

$A$ solid sphere rolls down without slipping on an inclined plane,then the percentage of rotational kinetic energy of the total energy will be ........ $\%.$