Two persons of masses $$55$$ kg and $$65$$ kg respectively, are at the opposite ends of a boat. The length of the boat is $$3.0$$ m and weighs $$100$$ kg. The $$55$$ kg man walks up to the $$65$$ kg man and sits with him. If the boat is in still water, the centre of mass of the system shifts by:
1. $$3.0$$ m
2. $$2.3$$ m
3. zero
4. $$0.75$$ m

Subtopic: Â Center of Mass |
Â 76%
From NCERT
AIPMT - 2012
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Three masses are placed on the $$x$$-axis: $$300~\text{g}$$ at origin, $$500~\text{g}$$ at $$x= 40~\text{cm}$$ and $$400~\text{g}$$ at $$x= 70~\text{cm}$$. The distance of the centre of mass from the origin is:
1. $$45~\text{cm}$$
2. $$50~\text{cm}$$
3. $$30~\text{cm}$$
4. $$40~\text{cm}$$

Subtopic: Â Center of Mass |
Â 81%
From NCERT
AIPMT - 2012
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Two particles that are initially at rest, move towards each other under the action of their mutual attraction. If their speeds are $$v$$ and $$2v$$ at any instant, then the speed of the centre of mass of the system will be:
1. $$2v$$
2. $$0$$
3. $$1.5v$$
4. $$v$$

Subtopic: Â Center of Mass |
Â 78%
From NCERT
AIPMT - 2010
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A man of $$50$$ kg mass is standing in a gravity-free space at a height of $$10$$ m above the floor. He throws a stone of $$0.5$$ kg mass downwards with a speed of $$2$$ ms-1. When the stone reaches the floor, the distance of the man above the floor will be:
1. $$9.9$$ m
2. $$10.1$$ m
3. $$10$$ m
4. $$20$$ m

Subtopic: Â Center of Mass |
Â 78%
From NCERT
AIPMT - 2010
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Given the following statements:

 1 The centre of gravity (C.G.) of a body is the point at which the weight of the body acts. 2 If the earth is assumed to have an infinitely large radius, the centre of mass coincides with the centre of gravity. 3 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. 4 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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Two bodies of mass $$1$$ kg and $$3$$ kg have position vectors $$\hat{i}+2\hat{j}+\hat{k}$$ and $$-3\hat{i}-2\hat{j}+\hat{k}$$ respectively. The centre of mass of this system has a position vector:
1. $$-2\hat{i}+2\hat{k}$$
2. $$-2\hat{i}-\hat{j}+\hat{k}$$
3. $$2\hat{i}-\hat{j}-2\hat{k}$$
4. $$-\hat{i}+\hat{j}+\hat{k}$$

Subtopic: Â Center of Mass |
Â 88%
From NCERT
AIPMT - 2009
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