System of Particles and Rotational Motion

A rod of linear mass density ' ' and length 'L' is bent to form a ring of radius 'R'. Moment of inertia of ring about any of its diameters is:

1. L38 2
2. L316 2
3. L34 2
4. L312

A thin solid disk of 1 kg is rotating along its diameter axis at the speed of 1800 rpm. By applying an external torque of 25 N m for 40 s, the speed increases to 2100 rpm. The diameter of the disk is m.

A rod of length 5 L is bent at right angle keeping one side length as 2 L. [figure] The position of the centre of mass of the system : (Consider L = 10 cm)

1. 4 i + 9 j
2. 2 i + 3 j
3. 5 i + 8 j
4. 3 i + 7 j

A, B and C are disc, solid sphere and spherical shell respectively with same radii and masses. These masses are placed as shown in figure. [figure] The moment of inertia of the given system about PQ axis is x15I, where I is the moment of inertia of the disc about its diameter. The value of x is .

Let M and R be the mass and radius of a disc. A small disc of radius R/3 is removed from the bigger disc as shown in figure. The moment of inertia of remaining part of bigger disc about an axis passing through the centre O and perpendicular to the plane of disc is 4xMR2. The value of x is . [figure]

Which of the following are correct expressions for torque acting on a body? ( r = position vector; p = linear momentum; L = angular momentum; = angular acceleration; I = moment of inertia; F = force; t = time) Choose the correct answer from the options given below:

1. A, B, D and E Only
2. C and D Only
3. B, C, D and E Only
4. B, D and E Only

A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is x5 where x = .

A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is 8 m/s. The speed of the particle on the rim of the wheel at the same level as the centre of the wheel, will be :

1. 4 2 m/s
2. 8 m/s
3. 4 m/s
4. 8 2 m/s

A solid sphere with uniform density and radius R is rotating initially with constant angular velocity ( 1) about its diameter. After some time during the rotation it starts losing mass at a uniform rate, with no change in its shape. The angular velocity of the sphere when its radius becomes R/2 is x 1. The value of x is .

A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg, kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is [figure]

1. 2.5 m/s2
2. 3.5 m/s2
3. 0.25 m/s2
4. 0.35 m/s2