The centre of mass of a body
Lies always outside the body
May lie within, outside of the surface of the body
Lies always inside the body
Lies always on the surface of the body
A constant torque acting on a uniform circular wheel changes its angular momentum from $L_0$ to $4L_0$ in $4\,s$ . The magnitude of this torque is
The centre of mass of a body
A thin wire of length $l$ and uniform linear mass density of $\rho $ is bent into a circular loop with centre $O$ and radius $r$ as shown in the figure. The moment of inertia of the loop about the axis $XX'$ is
A smooth uniform rod of length $L$ and mass $M$ has two identical beads of negligible size, each of mass $m$ , which can slide freely along the rod. Initially the two beads are at the centre of the rod and the system is rotating with angular velocity $\omega _0$ about its axis perpendicular to the rod and passing through its mid-point (see figure). There are no external forces. When the beads reach the ends of the rod, the angular velocity of the system 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