A disc of radius R rolls on a horizontal ground with linear acceleration $a$ and angular acceleration $\alpha$ as shown in Figure. The magnitude of acceleration of point P as shown in the figure at an instant when its linear velocity is v and angular velocity is $\omega$ will be

Two thin discs, each of mass $M$ and radius $r$ metre, are attached as shown in figure, to form a rigid body. The rotational inertia of this body about an axis perpendicular to the plane of disc $B$ passing through its centre is

Two identical masses are connected to a horizontal thin (massless) rod as shown in the figure. When their distance from the pivot is $D$, a torque $\tau$ produces an angular acceleration of ${\alpha }_1$. The masses are now repositioned, so that they are $2D$ from the pivot. The same torque produces an angular acceleration ${\alpha }_2$ which is given by, 

From a complete ring of mass $\mathrm{M}$ and radius $\mathrm{R}$, a $30°$ sector is removed. What is the moment of inertia of the incomplete ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is

A uniform disc of mass $M$ and radius $R$ is mounted on an axle supported in frictionless bearings. A light cord is wrapped around the rim of the disc and a steady downward pull $T$ is exerted on the cord. The angular acceleration of the disc is

Four spheres each having mass $m$ and radius $r$ are placed with their centres on the four corners of a square of side $a$. Then the moment of inertia of the system about an axis along one of the sides of the square is :-