System of Particles and Rotational Motion · Question 53

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)

A small mass attached to a string rotates on a frictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will [figure]

1. decrease by a factor of 2
2. remain constant
3. increase by a factor of 2
4. increase by a factor of 4

The instantaneous angular position of a point on a rotating wheel is given by the equation (t) = 2t3 - 6t2 The torque on the wheel becomes zero at

1. t = 1 s
2. t = 0.5 s
3. t = 0.25 s
4. t = 2 s

The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I0. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

1. I0 + ML2/2
2. I0 + ML2/4
3. I0 + 2ML2
4. I0 + ML2

From a circular disc of radius R and mass 9M, a small disc of mass M and radius R3 is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is

1. 409MR2
2. MR2
3. 4MR2
4. 49MR2

A solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?

1. Both together only when angle of inclination of plane is 45
2. Both together
3. Hollow cylinder
4. Solid cylinder

A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity . Two objects each of mass m are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by

1. (M+2m) 2m
2. 2M M+2m
3. (M+2m) M
4. M M+2m

Which one of the following pairs of statements is correct ?

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

A circular disk of moment of inertia It is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed i. Another disk of moment of inertia Ib is dropped coaxially onto the rotating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed . The energy lost by the initially rotating disc to friction is

1. 12 Ib2(It + Ib) i2
2. 12 It2(It + Ib) i2
3. Ib - It(It + Ib) i2
4. 12 Ib It(It + Ib) i2