Two masses m1 and m2, m1 > m2 are connected to the ends of massless rope and allowed to move as shown in the figure. The acceleration of the centre of mass assuming pulley is massless and frictionless, is

1.  m1 - m2m1 + m2g

2.  0

3.  m1 - m2m1 + m22g

4.  m1 + m2m1 - m22g

Subtopic:  Center of Mass |
 62%
From NCERT
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The speed of a uniform spherical shell after rolling down an inclined plane of vertical height h from rest is:

1.  \(\sqrt{\frac{10   g h}{7}}\)

2.    \(\sqrt{\frac{6   g h}{5}}\)

3.  \(\sqrt{\frac{4   g h}{5}}\)

4.  \(\sqrt{2   g h}\)

Subtopic:  Rolling Motion (OLD NCERT) |
 67%
From NCERT
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A uniform rod of mass m is bent into the form of a semicircle of radius R. The moment of inertia of the rod about an axis passing thorugh A and Perpendicular to the plane of paper is

1. 23MR2

2. MR2

3. 2MR2

4. 32MR2

Subtopic:  Moment of Inertia |
From NCERT
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A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity ω. Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be

1. MωM+4m

2.(M+4m)ωM

3. (M-4m)ωM+4m

4. Mω4m

Subtopic:  Angular Momentum |
 79%
From NCERT
PMT - 2003
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Let g be acceleration due to gravity on the surface of earth and T be the rotational kinetic energy of the earth. Suppose the earth's radius decreases by 2%. Keeping all other quantities same (even ω)

1.  g decreases by 2% and T decreases by 4%

2.  g decreases by 4% and T decreases by 2%

3.  g increases by 4% and T decreases by 4%

4.  g decreases by 4% and T increases by 4%

Subtopic:  Moment of Inertia |
 61%
From NCERT
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The angular momentum of a system of particles is conserved

1. when no external force acts upon the system

2. when no external torque acts upon the system

3. when no external impulse acts upon the system

4. when axis of rotation remains same

Subtopic:  Torque |
 86%
From NCERT
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One hollow and one solid cylinder of the same radius roll down on a smooth inclined plane. Then the foot of the inclined plane is reached by 

1.  solid cylinder earlier 

2.  hollow cylinder earlier 

3.  simultaneously both 

4.  the heavier earlier irrespective of being solid or hollow

Subtopic:  Rolling Motion (OLD NCERT) |
From NCERT
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ABC is an equilateral triangle with O as its cente. 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. 2(F1+F2)

Subtopic:  Torque |
 73%
From NCERT
PMT - 2012
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A circular platform is mounted a frictionless vertical axle. Its radius R = 2m and moment of inertia about the axle are 200 kgm2. It is initially at rest. A 50 kg man 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.  πs

2.  3π2s

3.  2πs

4.  π2s

Subtopic:  Angular Momentum |
 62%
From NCERT
PMT - 2012
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The motor of an engine is rotating about its axis with an angular velocity of 100 rpm.  It comes to rest is 15 s, after being switched off.  Assuming constant angular deceleration.  What are the numbers of revolutions made by it before coming to rest?

1. 12.5         

2. 40             

3. 32.6           

4. 15.6

Subtopic:  Rotational Motion: Kinematics |
 70%
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