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 |
 58%
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.  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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A cylinder of 500 g and radius 10 cm has moment of inertia (about its natural axis)

1. 2.5×10-3 kg-m2

2. 2×10-3 kg-m2

3. 5×10-3 kg-m2

4. 3.5×10-3 kg-m2

Subtopic:  Moment of Inertia |
 69%
From NCERT
PMT - 2001
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Two rings of the same radius and mass are placed such that their centers are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the center and perpendicular to the plane of one of the rings is (mass of the ring and radius = r)

1.  12mr2

2.  mr2

3.  32mr2

4.  2mr2

Subtopic:  Moment of Inertia |
 66%
From NCERT
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In a rectangle ABCD (BC = 2AB). The moment of inertia along which axis will be minimum?

1.  BC

2.  BD

3.  HF

4.  EG

               

Subtopic:  Moment of Inertia |
From NCERT

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A wheel comprises of a ring of radius R and mass M and three spokes of mass m each. The moment of inertia of the wheel about its axis is

                   

1.  M + m4R2

2.  M + mR2

3.  M + 3mR2

4.  M + m2R2

Subtopic:  Moment of Inertia |
 55%
From NCERT
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The angular velocity of a body changes from 125 rev./sec to 1 rev./sec. without applying any torque. The ratio of its radius of gyration in two situations is :

1.  5: 1

2.  1: 5

3.  1: 25

4.  25: 1

Subtopic:  Angular Momentum |
 65%
From NCERT
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