A dumbbell is placed in water of density `rho`. It is observed that by attaching a mass `m` to the rod, the dumbbell floats with the rod horizontal on the surface of water and each sphere exactly half submerged as shown in the figure. The volume of the mass `m` is negligible. The value of length `l` is

Two uniform thin rods each of length L and mass m are joined as shown in the figure. Find the distance of centre of mass the system from point O

A composite rod comprising two rods of mass m and 2m and each of length l = 1 m as shown in the figure. Assume omega = 10 rad//s and m = 1 kg , the KE of the rotating composite rod is. .

A rod of length / and of mass M and another rod of length 2/ and mass 2M are arranged as shown below in the figure.The magnitude of gravitational field at point P is

The moment of inertia of a thing uniform rod of length L and mass M , about axis CD (as shown in figure) is

A uniform cube of mass M is floating on the surface of a liquid with three fourth of its volume immersed in the liquid (density =rho) . The length of the side of the cube is equal to

Calculate the force exerted by point mass m on rod of uniformly distributed mass M and length l (Placed as shown in figure) .

Find the moment of inertia of the rod AB about an axis yy as shown in figure. Mass of the rod is m and length is l.

A uniform rod of length L and mass M is pulled horizontally on a smooth surface with a force F . Determine the elongation of rod if Young's modulus of the material is Y .

A rod of mass m and length L is hinged at its top end. If the rod is in equilibrium making an angle of 30^(@) with the vertical when a horizontal force F is applied as shown in figure, then the value of F is:

A hollow cylindrical pipe of mass M and radius R has a thin rod of mass m welded inside it, along its length. A light thread is tightly wound on the surface of the pipe. A mass m_(0) is attached to the end of the thread as shown in figure. The system stays in equilibrium when the cylinder is placed such that alpha = 30^(@) The pulley shown in figure is a disc of mass (M)/(2) (a) Find the direction and magnitude of friction force acting on the cylinder. (b) Express mass of the rod ‘m’ in terms of m_(0)