Systems of Part...

A uniform cylinder has a radius R and length L. If the moment of inertia of this cylinder about an axis passing through its centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through its centre and perpendicular to its length, then

The rectangular block shown in the figure is rotated in turn about x – x, y – y and z – z axis passing through its centre of mass O. Its moment of inertia is

From an inclined plane a sphere a disc, a ring and a spherical shell are rolled without slipping. The order of their reaching at the base will be

A wheel of moment of inertia 5 × 10^–3 kg–m² is making 20 revolutions/sec. The torque required to stop it in 10 sec is

If all of a sudden the radius of the earth decreases, then

A particle of mass m = 5 units is moving with a uniform speed v = 3√2 units in the XOY plane along the straight line Y = X + 4. The magnitude of the angular momentum about origin is

A sphere of mass 50 g and diameter 20 cm rolls without slipping with a velocity of 5cm/sec. Its total kinetic energy is

Five particles of mass 2 kg are attached to the rim of a circular disc of radius 0.1 m and negligible mass. Moment of inertia of the system about the axis passing through the centre of the disc and perpendicular to its plane is

The moment of inertia of a metre scale of mass 0.6 kg about an axis perpendicular to the scale and located at the 20 cm position on the scale in kg m² is (Breadth of the scale is negligible)

Four thin rods of same mas M and same length l, form a square as shown in figure. Moment of inertia of this system about an axis through centre O and perpendicular to its plane is