$A$ string breaks if its tension exceeds $10 \, N$. $A$ stone of mass $250 \, g$ tied to this string of length $10 \, cm$ is rotated in a horizontal circle. The maximum angular velocity of rotation can be .......... $rad/s$.

$A$ motorcycle is moving on an overbridge of radius $R$. The driver maintains a constant speed $v$. As the motorcycle is ascending on the overbridge,the normal force on it is

$A$ particle is moving with a uniform speed in a circular orbit of radius $R$ in a central force inversely proportional to the $n^{th}$ power of $R$. If the period of rotation of the particle is $T$,then

The end $B$ of the rod $AB$ which makes an angle $\theta$ with the floor is being pulled with a constant velocity $v_0$ as shown. The length of the rod is $l$. At the instant when $\theta = 37^o$,then:

$A$ particle moves with constant angular velocity in a circular path of a certain radius and is acted upon by a certain centripetal force $F$. If the centripetal force $F$ is kept constant but the angular velocity is doubled,the new radius of the path (original radius $R$) will be:

$A$ small disc is placed on the top of a smooth hemisphere of radius $R$. What is the smallest horizontal velocity $v$ that should be given to the disc for it to leave the hemisphere immediately at the top and not slide down it? [There is no friction]