Multiple Choice Questions on Centre of Mass

A metallic sphere of mass 1kg and radius 5 cm is welded to the end B of a thin rod AB of length 50 cm and mass 0.5 kg as shown. This rod with the sphere will balance horizontally on a knife edge placed at a distance ‘x’ from the end A of the rod if ‘x’ is equal to

(a) 35cm (b) 40 cm (c) 45 cm (d) 48 cm (e) 52 cm

This system can be imagined to be made of two point masses of 0.5 kg and 1 kg located at the middle (centre of mass) of the original rod and the centre (centre of mass) of the sphere respectively. The distance between these point masses is 30 cm (half the length of rod + radius of the sphere).

The centre of mass of the system is at a distance ‘d’ from the 0.5 kg mass of the rod such that 0.5×d = (30–d)×1.

This gives d = 20 cm. The distance ‘x’ of this centre of mass from the end A of the rod is given by x = 25+d = 25+20 = 45 cm.

Therefore, the knife edge is to be placed at 45 cm from the end A [Option (c)].

Consider now the following MCQ which appeared in Kerala Medical Entrance 2005 question paper:

A cricket bat is cut at the location of its centre of mass as shown. Then,

(a) the two pieces will have the same mass

(b) the bottom piece will have larger mass

(c) the handle piece will have larger mass

(d) mass of handle piece is double the mass of bottom piece

(e) cannot say

There is more material near the bottom end of the bat and you can compare it to the rod with the sphere we considered in the above question. The centre of mass of the bat is nearer the bottom end of the bat.

The bat will balance horizontally on a knife edge placed at the centre of mass. If the centre of mass of the handle piece and the bottom piece are at distances d₁ and d₂ respectively from the centre of mass of the entire bat, we have M₁d₁ = M₂d₂ where M₁ and M₂ are the masses of the handle piece and the bottom piece respectively. The distance d₁ is greater than d₂ since the handle piece has thinner regions compared to the bottom piece.Therefore, M₂ > M₁ [Option (b)].

You will find more multiple choice questions on centre of mass at physicsplus: Questions on Centre of Mass