Point masses `m_1` and `m_2` are placed at the opposite ends of a rigid rod of length L, and nelgligible mass. The rod is to be set rotating about an axis perpendicular to it. Find the position on this rod through which the axis should pass in order that the work required to set the rod rotating with angular velocity `omega_0` should be minimum.

The ends of a rod of length l move on two mutually perpendicular lines. Find the locus of the point on the rod which divides it in the ratio 1 : 2.

Two particles , each of mass m and charge q, are attached to the two ends of a light rigid rod of length 2 R . The rod is rotated at constant angular speed about a perpendicular axis passing through its centre. The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod

Calculate the radius of gyration of a rod of mass 100 g and length 100 m about an axis passing through is centre of gravity and perpendicular to its length.

A uniform rod a has mass M and length L.Its radius of gyration about an axis through its one end and perpendicuular to its length is :

Find the expression for moment of inertia of a thin uniform rod about an axis passing through its one end and perpendicular to its length.

A straight horizontal conducting rod of length 0.45 m and mass 60 g is suspended by two vertical wires at its ends. A current of 5.0 A is set up in the rod through the wires. What magnetic field should be set up normal to the conductor in order that the tension in the wires is zero?

Find the expression for moment of inertia of a thin uniform rod about an axis passing through its centre and perpendicular to its length

A steel rod of length 2l, cross sectional area A and mass M is set rotating in a horizontal plane about an axis passing through the centre. If Y is the Young's modulus for steel, find the extension in the length of the rod. (assume the rod is uniform).

A conducting rod PQ of length 20 cm and resistance 0.1 Omega rests on two smooth parallel rqails of negligible resistance AA' and CC'. It can slide on the rails and the arrangement is positioned betwaeen the poles of a permanent magnet producing unifrom magnetic field B=0.4 T. The rails, the rod and the magneitc field are in the three mutually perpendicular directions as shown in the figure. if hte ends A and C of the rails are short cicuited, find the External force required to move the rod with uniform velocity v=10cm/s.

A conducting rod PQ of length 20 cm and resistance 0.1 Omega rests on two smooth parallel rqails of negligible resistance AA' and CC'. It can slide on the rails and the arrangement is positioned betwaeen the poles of a permanent magnet producing unifrom magnetic field B=0.4 T. The rails, the rod and the magneitc field are in the three mutually perpendicular directions as shown in the figure. if hte ends A and C of the rails are short cicuited, find the Power required to move the rod with velocity v= 10 cm/s