System of Particles and Rotational Motion

The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle without slipping and slipping down the incline without rolling is

1. 5 : 7
2. 2 : 3
3. 2 : 5
4. 7 : 5

A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is [figure]

1. 2gL
2. 2g3L
3. 3g2L
4. gL

A small object of uniform density rolls up a curved surface with an initial velocity 'v'. It reaches upto a maximum height of 3v24g with respect to the initial position. The object is

1. hollow sphere
2. disc
3. ring
4. solid sphere

The ratio of radii of gyration of a circular ring and a circular disc, of the same mass and radius, about an axis passing through their centres and perpendicular to their planes are

1. 1 : 2
2. 3 : 2
3. 2 : 1
4. 2 : 1

Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D1 has 2 kg mass and 0.2 m radius and initial angular velocity of 50 rad s-1. Disc D2 has 4 kg mass, 0.1 m radius and initial angular velocity of 200 rad s-1. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad s-1) of the system is

1. 60
2. 100
3. 120
4. 40

A circular platform is mounted on a frictionless vertical axle. Its radius R = 2 m and its moment of inertia about the axle is 200 kg m2. It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1 m s-1 relative to the ground. Time taken by the man to complete one revolution is

1. s
2. 3 2 s
3. 2 s
4. 2 s

The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through [figure]

1. B
2. C
3. D
4. A

Three masses are placed on the x-axis : 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70 cm. The distance of the centre of mass from the origin is :

1. 40 cm
2. 45 cm
3. 50 cm
4. 30 cm

A solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity 4 m s-1. It collides with a horizontal spring of force constant 200 N m-1. The maximum compression produced in the spring will be

1. 0.5 m
2. 0.6 m
3. 0.7 m
4. 0.2 m

When a mass is rotating in a plane about a fixed point, its angular momentum is directed along

1. a line perpendicular to the plane of rotation
2. the line making an angle of 45 to the plane of rotation
3. the radius
4. the tangent to the orbit