$A$ 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 .... .

$A$ sphere of radius $a$ and mass $m$ rolls along a horizontal plane with constant speed $v_{0}$. It encounters an inclined plane at angle $\theta$ and climbs upward. Assuming that it rolls without slipping,how far up the sphere will travel?

$A$ hollow cylinder and a solid cylinder,initially at rest at the top of an inclined plane,are rolling down without slipping. If the time taken by the hollow cylinder to reach the bottom of the inclined plane is $2 \ s$,the time taken by the solid cylinder to reach the bottom of the inclined plane is: (in $s$)

Which of the following is true about the angular momentum of a cylinder rolling down a slope without slipping?

$A$ solid sphere rolling without friction on a horizontal surface with a constant speed of $2 \,m/s$, rolls up on an inclined ramp which is inclined at $30^{\circ}$. The maximum distance travelled by the sphere on the inclined ramp is (acceleration due to gravity $g=10 \,m/s^2, \sin 30^{\circ}=1/2$) (in $\,m$)

$A$ solid disc of radius $a$ and mass $m$ rolls down without slipping on an inclined plane making an angle $\theta$ with the horizontal. The acceleration of the disc will be $\frac{2}{b} g \sin \theta$ where $b$ is $........$. (Round off to the Nearest Integer)
($g =$ acceleration due to gravity)
($\theta =$ angle as shown in figure)