A system of two identical rods (L-shaped) of mass `m` and length `l` are resting on a peg `P` as shown in the figure. If the system is displaced in its plane by a small angle `theta`,find the period of oscillations:

Four identical uniform thin rods, each of mass m and length l are joined to a common point O as shown in the figure. Moment of inertia of the system about an axis passing through O and lying in the plane of rods is

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.

A spring of stiffness constant k and natural length l is cut into two parts of length 3l//4 and l//4 , respectively, and an arrangement is made as shown in figure . If the mass is slightly displaced , find the time period of oscillation.

A spring of stiffness constant k and natural length l is cut into two parts of length 3l//4 and l//4 , respectively, and an arrangement is made as shown in figure . If the mass is slightly displaced , find the time period of oscillation.

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.

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.

Four thin rods of same mass m and same length L form a square as shown in the figure. M.I. of this system about an axis through center O and perpendicular to its plane is

Two identical thin uniform rods of length L each are joined to form T shape as shown in the figure. The distance of centre of mass from D is

Two identical uniform rods of length l are joined to from L shaped frame, as shown is Fig. Locate the centre of mass of the frame.