A cylinder of mass m and radius R rolls down on an inclined plane of inclination $$\theta$$. Calculate the linear acceleration of axis of cylinder.
Two identical ladders, each of mass M and length L are resting on the rough horizontal surface as shown in the figure. A block of mass $$m$$ hangs from P. If the system is in equilibrium, find the magnitude and the direction of frictional force at A and B.

One quarter section is cut from a uniform circular disc of radius $R$. This section has a mass $M$. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is

A thin wire of length $L$ and uniform linear mass density $\rho$ is bent into a circular loop with centre at $O$ as shown. The moment of inertia of the loop about the axis $XX'$ is:

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