$A$ 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 $(a)$ & $(b)$.
$1$
$\frac{9}{{10}}$
$\frac{{10}}{9}$
none
As shown in figure, a mass $m$ = $500\ g$ hangs from the rim of a wheel of radius $r$ = $20\ cm$. When released from rest, the mass falls $2.0\ m$ in $8\ sec$. Then moment of inertia of the wheel is.......... $kg-m^2$. $(g = 10\ m/s^2)$
A mass $'m'$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R$. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?
A non-uniform bar of weight $W$ is suspended at rest by two strings of negligible weight as shown in Figure. The angles made by the strings with the vertical are $36.9^{\circ}$ and $53.1^{\circ}$ respectively. The bar is $2\; m$ long. Calculate the distance $d$ of the centre of gravity of the bar from its left end.
The spool shown in figure is placed on rough horizontal surface and has inner radius $r$ and outer radius $R$. The angle $\theta$ between the applied force and the horizontal can be varied. The critical angle $(\theta )$ for which the spool does not roll and remains stationary is given by
$A$ man can move on a horizontal plank supported symmetrically as shown. The variation of normal reaction on support $A$ with distance $x$ of the man from the end of the plank is best represented by :