$A$ tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega$. The force exerted by the liquid on the tube at the other end is

$A$ 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, then with what acceleration will the mass be released? (Assume $g =$ acceleration due to gravity)

$A$ ring has inner radius $R_1$ and outer radius $R_2$. It rolls without slipping with a constant angular velocity $\omega$. What is the ratio of the forces $F_1/F_2$ experienced by two particles located on the inner and outer surfaces of the ring?

$A$ binary star system consists of two stars,one of which has double the mass of the other. The stars rotate about their common centre of mass:

$A$ rigid rod of length $\ell$ is sliding. At some instant,the position of the rod is as shown in the figure. End $A$ has a constant velocity $v_0$ along the $x$-axis. At $t = 0$,the rod is vertical with end $B$ at $y = \ell$. Which of the following statements is correct?

$A$ bob of mass $m$ is tied by a massless string whose other end is wound on a flywheel (disc) of radius $R$ and mass $m$. When released from rest,the bob starts falling vertically downwards. If the bob has covered a vertical distance $h$,then the angular speed of the wheel will be (There is no slipping between the string and the wheel,$g$ is the acceleration due to gravity).