# 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 ${\mathrm{I}}_{\mathrm{z}}={\mathrm{I}}_{\mathrm{x}}+{\mathrm{I}}_{\mathrm{y}}$ (b) The moment of inertia of cube about z'-axis is ${\mathrm{I}}_{\mathrm{z}}\text{'}={\mathrm{I}}_{\mathrm{z}}+\frac{{\mathrm{ma}}^{2}}{2}$ (c) The moment of inertia of cube about z"-axis is $={\mathrm{I}}_{\mathrm{z}}+\frac{{\mathrm{ma}}^{2}}{2}$ (d)  Choose the correct statements: 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 |
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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 |
Â 57%
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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 |
Â 80%
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Consider the following statements.
 A: A body is in translational equilibrium if the net force on it is zero. B: A body is in rotational equilibrium if the net torque about any point is zero.
Choose the correct statements:
 1 (A) only 2 (B) only 3 both (A) and (B) 4 neither (A) nor (B)
Subtopic: Â Rotational Motion: Dynamics |
Â 80%
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Given below are two statements:
 Assertion (A): The center 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 center 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 |
Â 75%
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A uniform rod of mass $$M$$ and length $$L$$ lies at rest on a smooth horizontal plane, as shown in the figure. A particle of mass $$m,$$ moving with an initial velocity $$u$$ strikes one end $$(A)$$ of the rod and stops. The initial velocity $$u$$ is perpendicular to the length $$(AB)$$ of the rod.

Consider the following statements:
 P. Momentum of the system is conserved. Q. Kinetic energy of the system does not change after the collision. R. Angular momentum of the system is conserved.

1. P, Q, R are true.
2. P, R are true.
3. Only R is true.
4. Only P is true.
Subtopic: Â Angular Momentum |
Â 50%
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A block of mass $$m$$ is placed atop another block of mass $$M,$$ and the combination is at rest on a smooth horizontal table. A force $$F_1$$ is applied to $$m$$ and another force $$F_2$$ is applied to $$M,$$ the two acting horizontally and in opposite directions. Consider the following statements about the acceleration $$(a_{cm})$$ of the centre of mass of the system). (Take right as positive)

 A. $$a_{cm}=\dfrac{F_1-F_2}{m+M},$$ if there is no friction acting between  $$m$$ and  $$M$$ B. $$a_{cm}=\dfrac{F_1-F_2}{m+M},$$ if there is static friction between   $$m$$ and  $$M$$ C. $$a_{cm}=\dfrac{F_1-F_2}{m+M},$$ in all situations

Choose the most appropriate option:
 1 only (A) is true. 2 only (B) is true. 3 (C) is true. 4 (A), (B) are true but (C) is false.
Subtopic: Â Center of Mass |
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