A small $100$ $g$ sleeve $B$ can slide on a smooth, circular and rigid wire frame $A$ of radius $5$ $m$ placed in vertical place. The wire frame is rotating about its vertical diameter at $2$ $rad/s$. When the sleeve is brought at a particular angular position other than the bottom and the top of the ring, the sleeve will not slide on the wire frame. ……… $N$ is force of interaction between the sleeve and the wire frame at this position.

$A$ sphere is placed rotating with its centre initially at rest ina corner as shown in figure $(a)$ & $(b)$. Coefficient of friction between all surfaces and the sphere is $\frac{1}{3}$. Find the ratio of the frictional force $\frac{{{f_a}}}{{{f_b}}}$ by ground in situations $(a)$ & $(b)$.

$A$ horizontal force $F = mg/3$ is applied on the upper surface of a uniform cube of mass $‘m’$ and side $‘a’$ which is resting on a rough horizontal surface having $\mu_S = 1/2$. The distance between lines of action of $‘mg’$ and normal reaction $‘N’$ is :

In an experiment with a beam balance on unknown mass $m$ is balanced by two known mass $m$ is balanced by two known masses of $16\, kg$ and $4\, kg$ as shown in figure. The value of the unknown mass $m$ is ……. $kg$.

A massless string is wrapped round a disc of mass $M$ and radius $R$. Another end is tied to a mass $m$ which is initially at height $h$ from ground level as shown in the fig. If the mass is released then its velocity while touching the ground level will be