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 |
 62%
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) |
 77%
From NCERT
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From a uniform square plate of side \(a\) and mass \(m\), a square portion \(DEFG\) of side \(\frac{a}{2}\) is removed. Then, the moment of inertia of the remaining portion about the axis \(AB\) is:

                
1. \(\dfrac{7ma^2}{16}\)
2. \(\dfrac{3ma^2}{16}\)
3. \(\dfrac{3ma^2}{4}\)
4. \(\dfrac{9ma^2}{16}\)

Subtopic:  Moment of Inertia |
 53%
From NCERT
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The centre of the mass of \(3\) particles, \(10\) kg, \(20\) kg, and \(30\) kg, is at \((0,0,0)\). Where should a particle with a mass of \(40\) kg be placed so that its combined centre of mass is \((3,3,3)\)?
1. \((0,0,0)\)
2. \((7.5, 7.5, 7.5)\)
3. \((1,2,3)\)
4. \((4,4,4)\)

Subtopic:  Center of Mass |
 76%
From NCERT
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The position of a particle is given by \(\vec r = \hat i+2\hat j-\hat k\) and momentum \(\vec P = (3 \hat i + 4\hat j - 2\hat k)\). The angular momentum is perpendicular to:

1. X-axis
2. Y-axis
3. Z-axis
4. Line at equal angles to all the three axes

Subtopic:  Angular Momentum |
 63%
From NCERT
PMT - 2000
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A body falling vertically downward under gravity breaks into two parts of unequal masses. The center of mass of the parts taken together shifts horizontally towards

1.  heavier piece 

2.  lighter piece 

3.  does not shift horizontally 

4.  depends on the vertical velocity at the time of breaking 

Subtopic:  Center of Mass |
 59%
From NCERT
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A particle of mass m moves along line PC with velocity v as shown. What is the angular momentum of the particle about O

             

1. \(\text {mvL}\)

2. \(mvl\)

3. \(mvr\)

4. \(0\)

Subtopic:  Angular Momentum |
 76%
From NCERT
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A solid sphere, disc, and solid cylinder all of the same mass and made up of the same material are allowed to roll down (from rest) on an inclined plane, then,

1. solid sphere reaches the bottom first.
2. solid sphere reaches the bottom late.
3. the disc will reach the bottom first.
4. all of them reach the bottom at the same time.

Subtopic:  Rolling Motion (OLD NCERT) |
 79%
From NCERT
PMT - 2010
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