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Q. No.
A uniform ladder of mass \(10\) kg is placed at an angle against a frictionless vertical wall, as shown in the figure, by applying a horizontal force \(F\) at the bottom \((B)\) of the ladder, towards the wall. (Take \(g=10\) m/s2).

Assume that the ground is frictionless. The force \(F\) equals:
1. \(100\sqrt3\) N 2. \(50\sqrt3\) N
3. \(\dfrac{100}{\sqrt3}\) N 4. \(\dfrac{50}{\sqrt3}\) N
Subtopic:  Torque |
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A block \(A\) is pushed on a smooth horizontal plane by applying a horizontal force \(F ,\) which causes an acceleration of \({\dfrac g 4}\) (\(g\): acceleration due to gravity). The block does not topple, even though the force acts at its highest point. The normal reaction shifts forward by:
                
1. \({\dfrac b 2}\) 2. \({ \dfrac b 4}\)
3. \({\dfrac b 8}\) 4. \(\dfrac b 3\)
Subtopic:  Torque |
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A uniform cylinder of mass \(M,\) radius \(R\) and height \(3R\) is placed upright on a horizontal surface. A particle of mass \(m\) is placed on the top of the cylinder at its edge. For what minimum value of \(m\) will the cylinder topple? 
                      
1. \(m = 3M\)
2. \(m= \dfrac {M}{3}\)
3. \(m= \dfrac {3M }{2}\)
4. No value of \(m\) will cause the cylinder to topple.
Subtopic:  Torque |
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A uniform ladder \(AB\) is placed against a frictionless vertical wall, with the bottom of the ladder on a rough horizontal surface – as shown in the figure. A \(30~\text{kg}\) boy, whose weight is equal to that of the ladder, climbs up to the very top \(A.\) The system remains stable. The normal reaction at \(A\) equals: \((g=10~\text{m/s}^2)\)
                               
1. \(150~\text{N}\) 2. \(450~\text{N}\)
3. \(600~\text{N}\) 4. \(800~\text{N}\)
Subtopic:  Torque |
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A horizontal force \(F\) is applied to a uniform solid sphere at rest, so that its line of action passes through the mid-point (\(P\)) of the vertical radius \(OA;O\) being the centre of the sphere (mass : \(m\)). The acceleration of the uppermost point \(A\) is:
          
 
1. equal to \(\dfrac{F}{m}.\)
2. greater than \(\dfrac{F}{m}.\)
3. less than \(\dfrac{F}{m}.\)
4. unpredictable, and depends on the radius of the sphere.
Subtopic:  Torque |
 57%
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A uniform solid wheel of mass \(m,\) radius \(R\) encounters a rectangular step of height \(h.\) The torque of the weight \(mg,\) of the wheel, about the forward edge of the step (\({A}\)) is (in magnitude):
                    
1. \(mgR\)
2. \(mg(R-h)\)
3. \(mgh\)
4. \(mg\)\(\sqrt{h(2R-h)}\)

Subtopic:  Torque |
 55%
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Given below are two statements: 

Assertion (A): Angular momentum of an isolated system of particles is conserved.
Reason (R): The net torque on an isolated system of particles is zero and the rate of change of angular momentum equals the torque.
 
1. Both (A) and (R) are True and (R) is the correct explanation of (A).
2. Both (A) and (R) are True but (R) is not the correct explanation of (A).
3. (A) is True but (R) is False.
4. (A) is False but (R) is True.
Subtopic:  Torque |
 80%
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A uniform disc of mass \(M\) and radius \(R\) is fixed, so that it is free to rotate in its own plane, about the centre \(O.\) A force \(F\) is applied tangentially to the disc, continuously, for one complete revolution, starting from rest.
               
The angular acceleration \((\alpha)\) of the disc is:
1. \(\dfrac{F}{2MR}\) 2. \(\dfrac{F}{MR}\)
3. \(\dfrac{2F}{MR}\) 4. \(\dfrac{3F}{2MR}\)
Subtopic:  Torque |
 71%
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A uniform rod \((AB)\) of mass \(4~\text{kg}\) and length \(1.5~\text m,\) lies on a smooth horizontal surface. An impulse of \(6~\text{N-s}\) is delivered to the end \(A\) of the rod, perpendicular to \(AB,\) at the initial instant \((t=0).\)

After what minimum time will the speeds of the ends \(A,B \) become equal?
1. \(\dfrac{\pi}{3}~\text s\) 2. \(\dfrac{\pi}{6}~\text s\)
3. \(\dfrac{\pi}{12}~\text s\) 4. \(\dfrac{\pi}{4}~\text s\)
Subtopic:  Torque |
 53%
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