A mass m moves in a circle on a smooth horizontal plane with velocity v0 at a radius R0. The mass is attached to a string that passes through a smooth hole in the plane as shown. 
 
The tension in the string is increased gradually and finally m moves in a circle of radiusR02. The final value of the kinetic energy is:
1. mv02
2. 14mv02
3. 2mv02
4. 12mv02

Subtopic:  Angular Momentum |
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A force F=αi^+3j^+6k^ is acting at a point r=2i^-6j^-12k^. The value of α for which angular momentum about the origin is conserved is:

1. -1

2. 2

3. zero

4. 1

Subtopic:  Angular Momentum |
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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 45o to the plane of rotation

3. the radius

4. the tangent to the orbit

Subtopic:  Angular Momentum |
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A circular platform is mounted on a frictionless vertical axle. Its radius R = 2m and its moment of intertia 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 ms-1 relative to the ground. Time taken by the man to complete one revolution is -

1.  3π2s

2.  2π s

3.  π2s

4.  π s

Subtopic:  Angular Momentum |
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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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A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity ω. 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. 2MωM+2m

2. (M+2m)ωM

3. MωM+2m

4. (M+2m)ω2m

Subtopic:  Angular Momentum |
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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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A particle of mass m moves in the XY plane with a velocity v along the straight line AB. If the angular momentum of the particle with respect to origin O is LA when it is at A and LB when it is at B, then: 
         

1. LA>LB

2. LA=LB

3. the relationship between LA and LB depends upon the slope of the line AB

4. LA<LB

Subtopic:  Angular Momentum |
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