Question

Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates (0,0)cm and (x,0)cm respectively. The block of 10 kg is moved on the same line through a distance of 6 cm towards the other block. The distance through which the block of 30 kg must be moved to keep the position of centre of mass of the system unchanged is :

A. 4 cm towards the 10 kg block
B. 2 cm away from the 10 kg block
C. 2 cm towards the 10 kg block
D. 4 cm away from the 10 kg block

Answer 1

The distance through which the block of 30 kg must be moved to keep the position of center of mass of the system unchanged is 2 cm towards the 10 kg block. (Option C).

How to calculate the distance the 30 kg mass must be moved?

The distance through which the block of 30 kg must be moved to keep the position of center of mass of the system unchanged is calculated by applying the principle of center mass as follows.

m₁r₁ = m₂r₂

where;

• m₁ is the mass of the 10 kg mass
• m₂ is the mass of the 30 kg mass
• r₁ is the position of mass m₁
• r₂ is the position of mass m₂

The distance through which the block of 30 kg must be moved is;

r₂ = (m₁r₁)/m₂

r₂ = ( 10 kg x 6 cm ) / ( 30 kg )

r₂ = 2 cm towards the 10 kg block