System of Parti...

A uniform disc of mass $m$, radius $r$ and a point mass $m$ are arranged as shown in the figure. The acceleration of point mass is : (Assume there is no slipping between pulley and thread and the disc can rotate smoothly about a fixed horizontal axis passing through its centre and perpendicular to its plane).

A uniform thin rod is bent in the form of closed loop $ABCDEFA$ as shown in the figure. The ratio of moment of inertia of the loop about x-axis to that about y-axis is

A square frame ABCD is formed by four identical rods each of mass 'm' and length 'T'. This frame is in X - Y plane such that side AB coincides with X - axis and side AD along Y - axis. The moment of inertia of the frame about X - axis is

Two thin discs each of mass $M$ and radius $R$ are placed at either end of a rod of mass $m$, length $l$ and radius $r$. Moment of inertia of the system about an axis passing through the centre of rod and perpendicular to its length is

In the figure shown, the plank is being pulled to the right with a constant speed $v$. If the cylinder does not slip then

Moment of inertia of a straight wire about an axis perpendicular to the wire and passing through one of its end is $I$. This wire is now framed into a circle (a ring) of single turn. The moment of inertia of this ring about an axis passing through centre and perpendicular to its plane would be:

A particle of mass $m$ is subjected to an attractive central force of magnitude $k/r^2$, $k$ being a constant. If at the instant when the particle is at an extreme position in its closed orbit, at a distance $a$ from the centre of force, its speed is $(k/2ma)$, if the distance of other extreme position is $b$. Find $a/b.$

Inside a smooth spherical shell of radius R a ball of the same mass is released from the shown position ( fig. ). Find the distance travelled by the shell on the horizontal floor when the ball comes to the just opposite position of itself with respect to its position in the shell. 

Find the moment of inertia of the rod AC about an axis BD as shown in figure. Mass of the rod is m and length is L

A mass $m$ is moving with constant velocity parallel to the $x$ axis. Its angular momentum w.r.t the origin