An automobile moves on a road with a speed of 54 kmh-1. The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis of rotation is 3 kg-m2. If the vehicle is brought to rest in 15 s, the magnitude of average torque transmitted by its brakes to the wheel is:

1. 6.66 kg m2 s-2

2. 8.58 kg m2 s-2

3. 10.86 kg m2 s-2

4. 2.86 kg m2 s-2

Subtopic:  Torque |
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A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound around the cylinder with one end attached to it and the other end hanging freely. The tension in the string required to produce an angular acceleration of 2 revolutions s-2 will be:

1. 25 N

2. 50 N

3. 78.5 N

4. 157 N

Subtopic:  Rotational Motion: Dynamics |
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The ratio of the acceleration for a solid sphere (mass 'm' and radius 'R') rolling down an incline of angle 'θ' without slipping and slipping down the incline without rolling is:

1. 5:7

2. 2:3

3. 2:5

4. 7:5

Subtopic:  Rolling Motion |
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A small object of uniform density rolls up a curved surface with an initial velocity ‘ν’. It reaches up to a maximum height 3v24g with respect to the initial position. The object is:
1. Solid sphere
2. Hollow sphere
3. Disc
4. Ring
Subtopic:  Rolling Motion |
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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 the figure. When the string is cut, the initial angular acceleration of the rod is: 
        
1. g/L
2. 2g/L
3. 2g/3L
4. 3g/2L

Subtopic:  Torque |
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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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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 center of mass of the system shifts by:

1. 3.0 m

2. 2.3 m

3. zero

4. 0.75 m

Subtopic:  Center of Mass |
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A solid cylinder of mass 3 kg is rolling on a horizontal surface with a velocity of 4 ms-1. It collides with a horizontal spring of force constant 200 Nm-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

Subtopic:  Rolling Motion |
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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 the magnitude of F3 is:
         

1. F1+F2

2. F1-F2

3. F1+F22

4. 2F+F2

Subtopic:  Torque |
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The instantaneous angular position of a point on a rotating wheel is given by the equation,
θ(t) = 2t3 – 6t2 
The torque on the wheel becomes zero at:

1.  t= 0.5 s

2.  t= 0.25 s

3.  t= 2 s

4.  t= 1 s

Subtopic:  Rotational Motion: Kinematics |
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