Four spheres,each of mass $M$ and diameter $2a$,are placed at the corners of a square of side $b$. The moment of inertia of this system about an axis along one of the sides of the square is:

$A$ block of mass $m$ is attached to a pulley disc of equal mass $m$ and radius $r$ by means of a slack string as shown. The pulley is hinged about its centre on a horizontal table and the block is projected with an initial velocity of $5\, m/s$. Its velocity when the string becomes taut will be

In the following problem,indicate the correct direction of the friction force acting on a cylinder of mass $M$ and radius $R$,which is pulled on a rough surface by a constant horizontal force $F$ applied at its center. The friction force can be represented by which of the following diagrams?

Inner and outer radii of a spool are $r$ and $R$ respectively. $A$ thread is wound over its inner surface and placed over a rough horizontal surface. The thread is pulled by a force $F$ as shown in the figure. Then,in the case of pure rolling:

One ice skater of mass $m$ moves with speed $2v$ to the right,while another of the same mass $m$ moves with speed $v$ toward the left,as shown in figure $I$. Their paths are separated by a distance $b$. At $t = 0$,when they are both at $x = 0$,they grasp a pole of length $b$ and negligible mass. For $t > 0$,consider the system as a rigid body of two masses $m$ separated by distance $b$,as shown in figure $II$. Which of the following is the correct formula for the motion after $t = 0$ of the skater initially at $y = b/2$?

The total kinetic energy of a body of mass $10 \ kg$ and radius $0.5 \ m$ moving with a velocity of $2 \ m/s$ without slipping is $32.8 \ J$. The radius of gyration of the body is .......... $m$.