In the following figure, a body of mass $m$ is tied at one end of a light string and this string and this string is wrapped around the solid cylinder of mass $M$ and radius $R$. At the moment $t = 0$ the system starts moving. If the friction is negligible, angular velocity at time $t$ would be
$\frac{{mgRt}}{{\left( {M + m} \right)}}$
$\frac{{2Mgt}}{{\left( {M + 2m} \right)}}$
$\frac{{2Mgt}}{{R\,\left( {M - 2m} \right)}}$
$\frac{{2mgt}}{{R\,\left( {M + 2m} \right)}}$
The mass per unit length of a rod of length $l$ is given by : $\lambda = \frac{M_0x}{l}$ ,where $M_0$ is a constant and $x$ is the distance from one end of the rod. The position of centre of mass of the rod is
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
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
A circular disc is rolling on a horizontal plane. Its total kinetic energy is $300\, J$. ........ $J$ is its translational $K.E.$
A tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both the ends. The tube is then rotated in a horizontal plane about one of its end with a uniform angular velocity $\omega$. The force exerted by the liquid at the other end is