If the linear density of a rod of length \(3 \text m\) varies as \(\lambda= \text{2+x} \), then the position of the center of mass of the rod is at a distance of:
1. \({7 \over 3}m\)
2. \({10 \over 7}m\)
3. \({12\over 7}m\)
4. \({9 \over 7}m\)

Subtopic:  Center of Mass |
 65%
From NCERT
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A sphere can not roll on:

1.  a smooth horizontal surface 

2.  a rough horizontal surface 

3.  a smooth inclined surface 

4.  a rough inclined surface 

Subtopic:  Rolling Motion (OLD NCERT) |
 56%
From NCERT
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Two balls are thrown simultaneously in the air. The acceleration of the center of mass of the two balls while in air 

1.  depends on the direction of the motion of the balls 

2.  depends on the masses of the two balls 

3.  depends on the speeds of two balls 

4.  is equal to g 

Subtopic:  Center of Mass |
 67%
From NCERT
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A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizotal and moment of inertia about it is I. A weight mg is attached to the end of the cord and falls from rest. After falling through a distance h, the angular velocity of the wheel will be

1. 2ghI+mr

2. 2mghI+mr2

3. 2mghI+2m12

4. 2gh

Subtopic:  Rolling Motion (OLD NCERT) |
 73%
From NCERT
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If a person standing on a rotating disc stretches out his hands, the angular speed will

1.  increase

2.  decrease

3.  remain same

4.  None of these

Subtopic:  Angular Momentum |
 85%
From NCERT
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If the earth were to suddenly contract to 1nth of its present size without any change in its mass, the duration of the new day will be nearly

1.  24/n hours

2.  24 n hours

3.  24/n2 hours

4.   24 n2 hours

Subtopic:  Angular Momentum |
 76%
From NCERT
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A sqaure lamina is as shown in figure. The moment of inertia of the frame about the three axes shown in figure are I1, I2 and I3 respectively. Select the correct alternative.

1. I2=I3>I1

2. I1>I2>I3

3. I2=I3<I1

4. I1<I2<I3

Subtopic:  Moment of Inertia |
 56%
From NCERT
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A particle performs uniform circular motion with an angular momentum L. If the frequency of the particle motion is double, the angular momentum becomes

1. 2L

2. 4L

3. L2

4. L4

Subtopic:  Angular Momentum |
 76%
From NCERT
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In figure (a), a meter stick, half of which is wood and the other half steel is pivoted at the wooden end at O and a force F is applied to the steel end a. In figure (b) the stick is pivoted at the steel eid at O' and the same force F is applied at the wooden end at a' The angular acceleration

1.  in (a) is greater than in (b)

2.  in (b) is greater than in (a)

3.  equal both in (a) and (b)

4.  none of the above.

Subtopic:  Torque |
 61%
From NCERT
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A 20 kg solid disc rolls on a horizontal surface at the rate of 4 ms-1. Its total kinetic energy is 

1.  60 J

2.  120 J

3.  240 J

4.  80 J

Subtopic:  Rolling Motion (OLD NCERT) |
 78%
From NCERT
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