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Q. No.Which of the following statements are correct?
(a)
centre of mass of a body always coincides with the centre of gravity of the body .
(b)
centre of gravity of a body is the point about which the total gravitational torque on the body is zero.
(c)
a couple on a body produce both translational and rotation motion in a body.
(d)
mechanical advantage greater than one means that small effort can be used to lift a large load.
1.
(a) and (b)
2.
(b) and (c)
3.
(c) and (d)
4.
(b) and (d)
Subtopic: Â Center of Mass |
 61%
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NEET - 2017
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A particle of mass \(m\) moves with a constant velocity along \(3\) different paths, \(DE, OA\) and \(BC\). Which of the following statements is not correct about its angular momentum about point \(O\)?
| 1. | It is zero when it is at \(A\) and moving along \(OA\). |
| 2. | The same at all points along the line \(DE\). |
| 3. | Of the same magnitude but oppositely directed at \(B\) and \(D\). |
| 4. | Increases as it moves along the line \(BC\). |
Subtopic: Â Angular Momentum |
 54%
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With reference to the figure of a cube of edge \(a\) and mass \(m,\) the following statements are given. (\(O\) is the centre of the cube).
| (a) | The moment of inertia of the cube about the \(z\)-axis is \(I_z=I_x+I_y\) |
| (b) | The moment of inertia of the cube about the \(z'\)-axis is \({I_z}'=I_z+\frac{{ma}^2}{2}\) |
| (c) | The moment of inertia of the cube about \(z''\)-axis is = \(=I_z+\frac{{ma}^2}{2}\) |
| (d) | \(I_x=I_y\) |
| 1. | (a, c) | 2. | (a, d) |
| 3. | (b, d) | 4. | (b, c) |
Subtopic: Â Moment of Inertia |
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Given the following statements:
| (a) | The centre of gravity (C.G.) of a body is the point at which the weight of the body acts. |
| (b) | If the earth is assumed to have an infinitely large radius, the centre of mass coincides with the centre of gravity. |
| (c) | To evaluate the gravitational field intensity due to any body at an external point, the entire mass of the body can be considered to be concentrated at its C.G. |
| (d) | The radius of gyration of any body rotating about an axis is the length of the perpendicular dropped from the C.G. of the body to the axis. |
Which one of the following pairs of statements is correct?
| 1. | (a) and (b) | 2. | (b) and (c) |
| 3. | (c) and (d) | 4. | (d) and (a) |
Subtopic: Â Center of Mass |
From NCERT
AIPMT - 2010
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Consider the following two statements:
| A: | The linear momentum of the system remains constant. |
| B: | The centre of mass of the system remains at rest. |
| 1. | A implies B and B implies A |
| 2. | A does not imply B and B does not imply A |
| 3. | A implies B but B does not imply A |
| 4. | B implies A but A does not imply B |
Subtopic: Â Center of Mass |
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Consider the following two statements:
| A: | The linear momentum of a system of particles is zero. |
| B: | The kinetic energy of a system of particles is zero. |
| 1. | A implies B and B implies A. |
| 2. | A does not imply B and B does not imply A. |
| 3. | A implies B but B does not imply A. |
| 4. | B implies A but A does not imply B. |
Subtopic: Â Center of Mass |
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Given below are two statements:
| Assertion (A): | If the sun were to 'suddenly' be removed, then the earth would continue to move around in its orbit. |
| Reason (R): | Angular momentum of a system of particles is conserved when there is no external torque. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Â Angular Momentum |
 58%
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Given below are two statements:
| Assertion (A): | Angular momentum of an isolated system of particles is conserved. |
| Reason (R): | The net torque on an isolated system of particles is zero and the rate of change of angular momentum equals the torque. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Â Torque |
 80%
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Given below are two statements:
Choose the correct option from the given ones:
1. (A) only
2. (B) only
3. both (A) and (B)
4. neither (A) nor (B)
| Statement A: | A body is in translational equilibrium if the net force on it is zero. |
| Statement B: | A body is in rotational equilibrium if the net torque about any point is zero. |
1. (A) only
2. (B) only
3. both (A) and (B)
4. neither (A) nor (B)
Subtopic: Â Rotational Motion: Dynamics |
 81%
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Given below are two statements:
| Assertion (A): | The centre-of-mass of an isolated system of particles remains at rest if it is initially at rest. |
| Reason (R): | Internal forces acting within a system cannot change the velocity of the centre-of-mass which is proportional to the total momentum of the system. |
| 1. | (A) is True but (R) is False. |
| 2. | (A) is False but (R) is True. |
| 3. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
Subtopic: Â Center of Mass |
 76%
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