The mass per unit length of a non-uniform rod of length L is given by μ=λx2 where λ is a constant and x is the distance from one end of the rod. The distance between the centre of mass of the rod and this end is:

1. L2

2. L4

3. 3L4

4. L3

Subtopic:  Center of Mass |
 71%
From NCERT
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At t = 0, the positions of the two blocks are shown. There is no external force acting on the system. Find the coordinates of the center of mass of the system at t = 3 seconds:
   

1. (1, 0) 2. (3, 0)
3. (4.5, 0) 4. (2.25, 0)
Subtopic:  Center of Mass |
 73%
From NCERT
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A uniform square plate ABCD has a mass of 10 kg. If two point masses of 5 kg each are placed at the corners C and D as shown in the adjoining figure, then the centre of mass shifts to the mid-point of:
          
1. OH

2. DH

3. OG

4. OF 

Subtopic:  Center of Mass |
 82%
From NCERT
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Four-point masses each of value \(m\) are placed at the corners of a square ABCD of side \(l\). The moment of inertia of this system about an axis passing through A and parallel to BD will be:

 

1. \(2ml^2\) 2. \(4ml^2\)
3. \(3ml^2\) 4. \(ml^2\)
Subtopic:  Moment of Inertia |
 54%
From NCERT
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A particle rotating on a circular path of the radius 4πm at 300 rpm reaches 600 rpm in 6 revolutions. If the angular velocity increases at a constant rate, find the tangential acceleration of the particle.

1. 10 m/s2

2. 12.5 m/s2

3. 25 m/s2

4. 50 m/s2

Subtopic:  Rotational Motion: Kinematics |
 57%
From NCERT
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A rod is falling down with constant velocity \(V_0\) as shown. It makes contact with hinge A and rotates around it. The angular velocity of the rod just after the moment when it comes in contact with hinge A is:

              

1. \(2 \mathrm{V}_0 / 3 \mathrm{L} \) 2. \(3 \mathrm{V}_0 / 2 \mathrm{L} \)
3. \(\mathrm{V}_0 / \mathrm{L} \) 4. \(2 \mathrm{V}_0 / 5 \mathrm{L}\)
Subtopic:  Angular Momentum |
 72%
From NCERT
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Two loads P1 and P2 (P1 >P2) are connected by a string passing over a fixed pulley. The center of gravity of loads are initially at the same height. Find the acceleration of the center of gravity of the system:
1. \(\left(\frac{(P_1-P_2)^{\frac{1}{2}}}{P_1+P_2}\right)\text{g}\)
2. \(\left(\frac{P_1-P_2}{P_1+P_2}\right)\text{g}\)
3. \(\left( \frac{P_1-P_2}{P_1+P_2}\right)^2 \text{g}\)
4. \(\left( \frac{P_1+P_2}{P_1-P_2}\right)\text{g}\)

Subtopic:  Center of Mass |
 58%
From NCERT
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A man hangs from a rope attached to a hot-air balloon. The man's mass is greater than the mass of the balloon and its contents. The system is stationary in the air. If the man now climbs up to the balloon using the rope, the centre of mass of the "man plus balloon" system will:

1. remain stationary 
2. move up
3. move down
4. first moves up and then return to its initial position

Subtopic:  Center of Mass |
 64%
From NCERT
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The law of conservation of angular momentum is valid when:

1. The net force is zero and the net torque is non-zero 2. The net force is non-zero and the net torque is non zero
3. Net force may or may not be zero and net torque is zero 4. Both force and torque must be zero
Subtopic:  Angular Momentum |
 72%
From NCERT
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The center of mass of a system of particles does not depend upon:

1. position of particles
2. relative distance between particles
3. masses of particles
4. force acting on the particle

Subtopic:  Center of Mass |
 67%
From NCERT
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