Two particles $A$ and $B$, of mass $M$ each are attached at the ends of a rigid massless rod of length $L$. A particle $\mathrm{P}$ of the same mass moving with a speed of $V$ at right angle to$\mathrm{AB}$  strikes $A$ and sticks to it. Then

A $T$ shaped object with dimensions shown in the Figure is lying on a smooth floor. A force $F$ is applied at the point $P$ parallel to $AB$, such that the object has only translational motion without rotation. Find the location of $P$ with respect to $C$.

Three identical spheres, each of mass $1 \mathrm{kg}$ are kept as shown in figure, Fig. 11.158 touching each other, with their centres on a straight line. If their centres are marked $P\mathit{,}\mathit{ }Q\mathit{,}\mathit{ }R$ respectively, the distance of centre of mass of the system from $P$ is

From a circular disc of radius $\mathrm{R}$ and mass $9\mathrm{M}$, a small disc of radius $\frac{R}{3}$ is removed, Fig. 11.159. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through $O$ is