Question

Masses 1 kg, 1.5 kg, 2 kg, and “M” kg are situated at (2,1,1), (1,2,1), (2,-2,1) and (-1,4,3). What is the value of “M” if their centre of mass is at (1,1,3/2)?

(a) 1 kg

(b) 1.5 kg

(c) 2 kg

(d) 2.5 kg

The question was asked by my college professor while I was bunking the class.

This intriguing question comes from System of Particles topic in section System of Particles and Rotational Motion of Physics – Class 11

Answer 1

Correct answer is (b) 1.5 kg

The explanation is: Sum of masses = 1 + 1.5 + 2 + M = 4.5 + M

x-coordinate;

(1*2 + 1.5*1 + 2*2 – M)/(4.5 + M) = 1

4.5 + M = 7.5 – M

2M = 3

M = 1.5 kg.