A mass $m$ hangs with the help of a string wrapped around a pulley on a firctionless bearing. The pulley has mass $m$ and radius $R$. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass $m$, if the string does not slip on the pulley, is:-
$\frac{2}{3} g$
$\frac{g}{3}$
$\frac{3}{2} g$
$g$
A disc of radius $20\, cm$ and mass half $kg$ is rolling on an inclined plane. Find out friction force so that disc performs pure rolling.
$A$ rod of weight $w$ is supported by two parallel knife edges $A$ and $B$ and is in equilibrium in a horizontal position. The knives are at a distance $d$ from each other. The centre of mass of the rod is at a distance $x$ from $A$.
A uniform disc is acted by two equal forces of magnitude F. One of them, acts tangentially to the disc, while other one is acting at the central point of the disc. The friction between disc surface and ground surface is $nF$. If $r$ be the radius of the disc, then the value of $n$ would be (in $N$ )
A mass $M= 40\ kg$ is fixed at the very edge of a long plank of mass $80\ kg$ and length $1\ m$ which is pivoted such that it is in equilibrium. How far (approx.) from the pivot should a mass of $100\ kg$ be attached so that the plank starts rotating with an angular acceleration of $1\ rad/s^2$?
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