Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. Hie cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time.

Moment of a solid cylinder about its axis of symmetry is equal to moment of inertia about an axis passing through its centre and perpendicular to its length.Show that L//r = sqrt3 .

Two spheres each of mass M and radius R//2 are connected with a massless rod of lenth 2R as shown in fig.What will be the oment of inertia of the system about an axis passing through the centre of one of the spheres and prependicular to the rod?

Why does a solid sphere have smaller moment of inertia than a hollow cylinder of same mass and radius, about an axis passing through their axes of symmetry?

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

Two sphere are of same mass and same external radius, one is solid and the other is hollow. Which one of them has larger moment of inertia about its diameter?

A string is wrapped around the rim of a wheel of moment of inertia 0.20 kg m^2 and radius 20 cm.the wheel is free to rotate about its axis .Initially,the wheel is at rest.The string is now pulled by a force of 20 N.Find the angular velocity of the wheel after 5.0 seconds.

A solid cylinder of mass 2kg and radius 20 cm is rotating about its axis with a frequency (10//pi)Hz .The rotational kinetic energy of the cylinder is :

A wheel in uniform motion about an axis passing through its centre and perpendicular to its plane is considered to be in mechanical (translational plus rotational equilibrium because no net external force or torque is required to sustain its motion. However, the particles that constitute the wheel do experience a centripetal acceleration directed towards the centre. How do you reconcile this fact with the wheel being in equilibrium? How would you set a half - wheel into uniform motion about an axis passing through the centre of mass of the wheel and perpendicular to its plane? Wil you require external forces to sustain the motion?

A small retangular coil ABCD contains 140 turns of wire. The sides AB and BC of the coil are of length 4.5 and 2.8 cm respectively, as shown in the figure The coil is held between the poles of a large magnet so that the coil can rotate about an axis thorugh its centre. The magnet produces a uniform magnetic field of flux density B between its poles. When the current in the coil is 170 mA, the maximum torque produced in the coil is 2.1 xx 10^-3 N m . For the coil in the position shown in the figure. calculate the magnitude of the force on (i) side AB of the coil and (ii) side BC of the coil.