A rod of weight \(w\) is supported by two parallel knife edges, A and B, and is in equilibrium in a horizontal position. The knives are at a distance \(d\) from each other. The centre of mass of the rod is at a distance \(x \) from A. The normal reaction to A is:
1. \(wx \over d\)
2. \(wd \over x\)
3. \(w(d-x) \over x\)
4. \(w(d-x) \over d\)

Subtopic:  Torque |
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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 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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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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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 uniform rod of length l and mass M is free to rotate in a vertical plane about A. The rod, initially in the horizontal position, is released. The initial angular acceleration of the rod is: (Moment of inertia of the rod about A isMl23)

1. 3g 2l

2. 2l3g

3. 3g2l2

4. mg12

Subtopic:  Torque |
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