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
$\frac{{M{\omega ^2}L}}{2}$
${M{\omega ^2}L}$
$\frac{{M{\omega ^2}L}}{4}$
$\frac{{M{\omega ^2}L^2}}{2}$
A ring of radius $4a$ is rigidly fixed in vertical position on a table. A small disc of mass $m$ and radius $a$ is released as shown in the fig. When the disc rolls down, without slipping, to the lowest point of the ring, then its speed will be
A wheel of radius $r$ rolls without slipping with a speed $v$ on a horizontal road. When it is at a point $A$ on the road, a small jump of mud separates from the wheel at its highest point $B$ and drops at point $C$ on the road. The distance $AC$ will be
Two spheres are rolling with same velocity (for their $C. M.$) their ratio of kinetic energy is $2 : 1$ & radius ratio is $2 : 1$, their mass ratio will be :
A ball is thrown on a lawn in such a way that it initially slides with a speed $v_0$ without rolling. It gradually picks up rotation motion. Find the speed of the ball at which there will be rolling without slipping-
A rigid body is rotating with variable angular velocity $(a -bt)$ at any instant of time $t.$ The total angle subtended by it before coming to rest will be ( $a$ and $b$ are constants)