System of Particles and Rotational Motion · Question 45

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

Two persons of masses 55 kg and 65 kg respectively, are at the opposite ends of a boat. The length of the boat is 3.0 m and weighs 100 kg. The 55 kg man walks up to the 65 kg man and sits with him. If the boat is in still water the centre of mass of the system shifts by:

1. 3.0 m
2. 2.3 m
3. zero
4. 0.75 m

ABC is an equilateral triangle with O as its centre. F1, F2 and F3 represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero then magnitude of F3 is [figure]

1. F1 + F2
2. F1 - F2
3. F1 + F22
4. 2(F1 + F2)