A small disc of radius 2 cm is cut from a disc of radius 6 cm. If the distance between their centres is 3.2 cm, what is the shift in the centre of mass of the disc?

1.  0.4 cm

2.  2.4 cm

3.  1.8 cm

4.  1.2 cm

Subtopic:  Center of Mass |
 63%
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From a circular disc of radius \(R\), a square is cut out with a radius as its diagonal. The distance of the centre of mass of the remainder from the centre of the disc is:
1. \(\frac{R}{(4\pi -2)}\)
2. \(\frac{R}{2\pi}\)
3. \(\frac{R}{(\pi -2)}\)
4. \(\frac{R}{(2\pi -2)}\)
Subtopic:  Center of Mass |
 58%
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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 P?

1. mvL                 

2. mvl               

3. mvr                 

4. zero

Subtopic:  Angular Momentum |
From NCERT
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Two bodies with moment of inertia I1 and I2 (I1>I2) and have equal angular momenta.  If KE of rotation are E1 and E2, then

1. E1=E2             

2. E1>E2               

3.  E1<E2             

4. E1E2

Subtopic:  Angular Momentum |
 75%
From NCERT
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Three indentical spheres, each of mass 1 kg are kept as shown in figure, touching each other, with their centres on a straight line. If their centres are marked P, Q, R respectively, the distance of centre of mass of the system from P is


1. \(   \frac{PQ   +   PR   +   QR}{3}\)
2. \(  \frac{PQ   + PR}{3}\)
3. \( \frac{PQ   + QR}{3}\)
4. \(   \frac{PR   +   QR}{3}\)

Subtopic:  Center of Mass |
 70%
From NCERT
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Two particles of equal mass have coordinates \((2~\text{m}, 4~\text{m}, 6~\text{m})\) and \((6~\text{m},2~\text{m},8~\text{m})\). Of these one particle has velocity \(v_1 = 2\hat i~\text{m/s}\) and another particle has velocity \(v_2 = 2\hat j ~\text{m/s}\) at time \(t=0\). The coordinate of their centre of mass at time \(t=1~\text{s}\) will be:
1. \((4~\text{m}, 4~\text{m}, 7~\text{m})\)
2. \((5~\text{m}, 4~\text{m}, 7~\text{m})\)
3. \((2~\text{m}, 4~\text{m}, 6~\text{m})\)
4. \((4~\text{m}, 5~\text{m}, 4~\text{m})\)

Subtopic:  Center of Mass |
 63%
From NCERT
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The M.I. of a body about the given axis is 1.2 kg x m2 initially the body at rest. In order to the rotational kinetic energy of 1500 J, the angular acceleration of 25 rad/sec2 must be about that axis for the duration of

1.  4 sec

2.  2 sec

3.  8 sec

4.  10 sec

Subtopic:  Rotational Motion: Kinematics |
 84%
From NCERT
PMT - 1996
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A loop rolls down on the inclined plane. The fraction of its total kinetic energy that is associated with rotational motion is

1.  \(1\over 2\)

2.  \(1\over 3\)
3.  \(3\over 2\)

4.  \(2\over 3\)

Subtopic:  Rolling Motion (OLD NCERT) |
 72%
From NCERT
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A ball kept in a closed box moves in the box making collisions with the walls. The box is kept on a smooth surface. The velocity of the centre of mass

1. of the box remains constant 

2. of the box plus the ball system remains constant

3. of the ball remains constant

4. of the ball relative to the box remains constant

Subtopic:  Center of Mass |
 67%
From NCERT
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A circular plate of diameter d is kept in contact with a square plate of an edge as shown in the figure. The density of the material and the thickness are the same everywhere. The center of mass of the composite system will be

                    

1. inside the circular plate 
2. inside the square plate
3. at the point of contact 
4. outside the system
Subtopic:  Center of Mass |
 64%
From NCERT
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