## Friday, April 01, 2011

### All India Pre-Medical/Pre-Dental Entrance Examination (Preliminary) 2010 (AIPMT 2010) Multiple Choice Questions on Centre of Mass

The following questions (MCQ) on centre of mass were included in the AIPMT 2010 question paper:

(1) 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 2 ms–1. When the stone reaches the floor, the distance of the man above the floor will be

(1) 20 m

(2) 9.9 m

(3) 10.1 m

(4) 10 m

You can work out this question either by using the concept of centre of mass or by applying the law of conservation of momentum.

The position of the centre of mass of the man-stone system will be unchanged as there are no external forces. If x is the distance of the man from the centre of mass when the stone reaches the floor, we have

50×x = 0.5×10 from which x = 0.1 m

As the centre of mass of the system is initially at a distance of 10 m above the floor, the distance of the man when the stone reaches the floor will be 10 + x = 10.1 m.

[You can apply the law of conservation of momentum and obtain the ‘recoil speed’ v of the man from the equation, 50×v = 0.5×2, from which v = 0.02 ms–1.

The time taken by the stone to reach the floor is 10/2 = 5 s. During this time the man will move up through a distance 0.02×5 = 0.1 m so that when the stone reaches the floor, the man will be at a distance 10 + 0.1 = 10.1 m above the floor].

(2) Two particles which are initially at rest move towards each other under the action of their internal attraction. If their speeds are v and 2v at any instant, then the speed of centre of mass of the system will be

(1) v

(2) 2 v

(3) zero

(4) 1.5 v

Since the particles are initially at rest, the speed of the centre of mass of the system is zero. Since there are no external forces on the system, the centre of mass will continue to be at rest even though the particles are moving under the action of their internal attraction. Therefore the correct option is (3).

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