Center Of Mass

Two bodies of mass kg and kg have position vectors and respectively. The centre of mass of this system has a position vector:
1.
2.
3.
4.

Two particles that are initially at rest, move towards each other under the action of their mutual attraction. If their speeds are and at any instant, then the speed of the centre of mass of the system will be:
1.
2.
3.
4.

A man of kg mass is standing in a gravity-free space at a height of m above the floor. He throws a stone of kg mass downwards with a speed of ms^-1. When the stone reaches the floor, the distance of the man above the floor will be:
1. m
2. m
3. m
4. m

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

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)

Three identical spheres, each of mass , are placed at the corners of a right-angle triangle with mutually perpendicular sides equal to (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of the centre of mass. 

1.		2.
3.		4.

Two objects of mass and respectively are connected to the two ends of a rigid rod of length with negligible mass. The distance of the center of mass of the system from the mass is:

1.		2.
3.		4.