A heavy ring of mass m is clamped on the periphery of a light circular disc. A small particle having equal mass is clamped at the centre of the disc. The system is rotated in such a way that the centre moves in a circle of radius r with a uniform speed v. We conclude that an external force

1. \(\frac{mv^2}{r}\) must be acting on the central particle

2. \(\frac{2mv^2}{r}\) must be acting on the central particle

3. \(\frac{2mv^2}{r}\) must be acting on the system

4. \(\frac{2mv^2}{r}\) must be acting on the ring

Subtopic:  Center of Mass |
From NCERT
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The centre of mass of a system of particles is at the origin. It follows that
(a). the number of particles to the right of the origin is equal to the number of particles to the left
(b). the total mass of the particles to the right of the origin is same as the total mass to the left of the origin
(c). the number of particles on \(x\)-axis should be equal to the number of particles on \(y\)-axis
(d). if there is a particle on the positive \(x\)-axis, there must be at least one particle on the negative \(x\)-axis

Choose the correct option:
1. (a), (b) and (c)
2. (a), (b) and (d)
3. All of these
4. None of these

Subtopic:  Center of Mass |
From NCERT
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A body has its centre of mass at the origin. The x–coordinates of the particles:

(a) may be all positive

(b) may be all negative

(c) may be all non-negative

(d) may be positive for some case and negative in other cases

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. All of these

Subtopic:  Center of Mass |
From NCERT
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In which of the following cases the centre of mass of a rod is certainly not at its centre?
 

a. the density continuously increases from left to right.
b. the density continuously decreases from left to right.
c. the density decreases from left to right upto the centre and then increases.
d. the density increases from left to right upto the centre and then decreases.

Choose the correct options:

1. (a) and (b)
2. (a), (b) and (c)
3. all of these
4. none of these

Subtopic:  Center of Mass |
 55%
From NCERT
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If the external forces acting on a system have zero resultant, the centre of mass:

(a) must not move

(b) must not accelerate

(c) may move

(d) may accelerate

Choose the correct options:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. All of these

Subtopic:  Center of Mass |
From NCERT
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A nonzero external force acts on a system of particles. The velocity and the acceleration of the centre of mass are found to be \(v_0\) and \(a_0\) at an instant \(t.\) It is possible that:
(a) \(v_0=0,\) \(a_0=0\)
(b) \(v_0=0,\) \(a_0 \neq0\)
(c) \(v_0 \neq0,\) \(a_0=0\)
(d) \(v_0 \neq0,\) \(a_0 \neq0\)
Choose the correct options:
1. (a) and (b)
2. (b) and (c)
3. (c) and (d)
4. (b) and (d)

Subtopic:  Center of Mass |
 51%
From NCERT
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Two balls are thrown simultaneously in the air. The acceleration of the centre of mass of the two balls while in the 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 the two balls.
4. is equal to \(g.\)
Subtopic:  Center of Mass |
 76%
From NCERT
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Let \(\overrightarrow A\) be a unit vector along the axis of rotation of a purely rotating body and \(\overrightarrow B\) be a unit vector along the velocity of a particle P of the body away from the axis. The value of \(\overrightarrow A.\overrightarrow B\) is:
1. \(1\)
2. \(-1\)
3. \(0\)
4. None of these

Subtopic:  Angular Momentum |
 78%
From NCERT
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A body is uniformly rotating about an axis fixed in an inertial frame of reference. Let \(\overrightarrow A\) be a unit vector along the axis of rotation and \(\overrightarrow B\) be the unit vector along the resultant force on a particle P of the body away from the axis. The value of \(\overrightarrow A.\overrightarrow B\) is:

1. 1

2. –1

3. 0

4. none of these

 74%
From NCERT
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A particle moves with a constant velocity parallel to the X-axis. Its angular momentum with respect to the origin:

1. is zero
2. remains constant
3. goes on increasing
4. goes on decreasing


 

Subtopic:  Angular Momentum |
 65%
From NCERT
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