Two rotating bodies $A$ and $B$ of masses $m$ and $2\,m$ with moments of innertia $I_A$ and $I_B\,(I_B > I_A)$ have equal kinetic energy of rotation. If $L_A$ and $L_B$ be their angular momentum respectively, then

A child is standing at one end of a long trolley moving with a speed $v$ on a smooth horizontal floor. If the child starts running towards the other end of the trolley with a speed $u$, the centre of mass of the system (trolley + child) will move with a speed.

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 rod of length $L$ is held vertically on a smooth horizontal surface. The top end of the rod is given a gentle push. At a certain instant of time, when the rod makes an angle $\theta$ with horizontal the velocity of $COM$ of the rod is $v_0$ . The velocity of the end of the rod in contact with the surface at that instant is 

A cockroach of mass $\frac {M}{2}$ is start moving, with velocity $V$ on the circumference of a disc of mass $'M'$ and $'R',$ what will be angular velocity of disc?

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