System of Particles and Rotational Motion · Question 35

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

Moment of inertia of a rod of mass 'M' and length 'L' about an axis passing through its center and normal to its length is ' '. Now the rod is cut into two equal parts and these parts are joined symmetrically to form a cross shape. Moment of inertia of cross about an axis passing through its center and normal to plane containing cross is :

1. /4
2. /8
4. /2

A square lamina OABC of length 10 cm is pivoted at 'O'. Forces act at lamina as shown in figure. If lamina remains stationary, then the magnitude of F is : [figure]

1. 10 N
2. 0 (zero)
3. 10 2 N
4. 20 N

A cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The mass of wheel is 10 kg and radius is 10 cm and it can freely rotate without any friction. Initially the wheel is at rest. If a steady pull of 20 N is applied on the cord, the angular velocity of the wheel, after the cord is unwound by 1 m, would be: [figure]

1. 20 rad/s
2. 30 rad/s
3. 10 rad/s
4. 0 rad/s

The moment of inertia of a circular ring of mass M and diameter r about a tangential axis lying in the plane of the ring is :

1. 38Mr2
2. 2Mr2
3. 12Mr2
4. 32Mr2