A thin rod of length $L$ and mass $M$ is bent at its mid-point into two halves so that the angle between them is $90^o$. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is
$\frac {ML^2}{6}$
$\frac {\sqrt 2ML^2}{24}$
$\frac {ML^2}{24}$
$\frac {ML^2}{12}$
A string is wrapped around a disc of mass $M$ and radius $R$ and the free end is fixed to ceiling. Centre of mass falls down as the disc unwinds the string. The tension in the string is
A solid sphere is rolling on a frictionless surface, shown in figure with a translational velocity $v\,\,m/s.$ If it is to climb the inclined surface then $v$ should be
Two loops $P$ and $Q$ are made from a uniform wire. The radii of $P$ and $Q$ are $r_1$ and $r_2$ respectively, and their moments of inertia are $I_1$ and $I_2$ respectively. If $I_2/I_1=4$ then $\frac{{{r_2}}}{{{r_1}}}$ equals
A man of $50\, kg$ mass is standing in a gravity free space at a heigth of $10\,m$ above the floor. He throws a stone of $0.5\, kg$ mass downwards with a speed of $2\,m/s$. When the stone reaches the floor, the distance of the man above the floor will be ........ $m.$
Two particles having mass $'M'$ and $'m'$ are moving in circular paths having radii $R$ and $ r.$ If their time periods are same then the ratio of their angular velocities will