A circular disk of a moment of inertia It is rotating in a horizontal plane, about its symmetric axis, with a constant angular speed ωi. Another disk of a 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 ωf. The energy lost by the initially rotating disc due to friction is:

1. 12Ib2It+Ibωi2

2. 12It2It+Ibωi2

3. 12Ib-ItIt+Ibωi2

4. 12IbItIt+Ibωi2

Subtopic:  Angular Momentum |
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Two particles that are initially at rest, move towards each other under the action of their mutual attraction. If their speeds are v and 2v at any instant, then the speed of the centre of mass of the system will be:

1. 2v

2. 0

3. 1.5v

4. v

Subtopic:  Center of Mass |
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A man of 50 kg mass is standing in a gravity-free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed of 2 ms-1. When the stone reaches the floor, the distance of the man above the floor will be:

1. 9.9 m

2. 10.1 m

3. 10 m

4. 20 m

Subtopic:  Center of Mass |
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If F is the force acting on a particle having position vector r and τ be the torque of this force about the origin, then:

1. r. τ≠ 0 and F. τ = 0

2. r. τ> 0 and F. τ< 0

3. r. τ = 0 and F. τ = 0

4. r. τ= 0 and F. τ≠ 0

Subtopic:  Torque |
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A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity ω. If two objects each of mass m are attached gently to the opposite ends of the diameter of the ring, the ring will then rotate with an angular velocity:

1. ω(M-2m)M+2m

2. ωMM+2m

3. ω(M+2m)M

4. ωMM+m

Subtopic:  Angular Momentum |
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Two bodies of mass 1 kg and 3 kg have position vectors i^+2j^+k^ and -3i^-2j^+k^ respectively. The centre of mass of this system has a position vector:
1. -2i^+2k^
2. -2i^-j^+k^
3. 2i^- j^- 2k^
4. -i^+j^+k^

Subtopic:  Center of Mass |
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Four identical thin rods, each of mass M and length l, form a square frame. The moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is:
1. 43Ml2
2. 23Ml2
3. 133Ml2
4. 13Ml2
Subtopic:  Moment of Inertia |
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The ratio of the radii of gyration of a circular disc to that of a circular ring, each of the same mass and radius, around their respective axes is:

1.  3 : 2

2.  1 : 2

3.  2 : 1

4.  2 : 3

Subtopic:  Moment of Inertia |
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A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is 90o. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is:

1.  ML224

2.  ML212

3.  ML26

4.  2ML224

Subtopic:  Moment of Inertia |
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A wheel has an angular acceleration of 3.0 rad/s2 and an initial angular speed of 2.00 rad/s. In a time of 2 s, it has rotated through an angle (in radian) of:

1. 6

2. 10

3. 12

4. 4

Subtopic:  Rotational Motion: Kinematics |
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