Four masses are fixed on a massless rod as shown in Fig. The moment of inertia about the axis $P$ is about ....... $kg-m^2$

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.

A uniform cube of side $a$ and mass $m$ rests on a rough horizontal table. A horizontal force $F$ is applied normal to one of the faces at a point that is directly above the centre of face, at a height $\frac {3a}{4}$ above the base. The minimum value of $F$ for which the cube begins to tilt about the edge is (Assume that the cube does not slide)

Two rings of the same radius and mass are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to the plane of one of the rings is : (mass of the ring $= m,$ radius $= r$ )

Radius of gyration of a body depends on

A thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega $ . Two objects each of mass $m$ are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity