Question

Two particles of masses 10kg and 30kg are lying on a straight line. The 10kg mass is shifted towards the 30kg mass by a distance of 2cm. By what distance should the 30kg mass be shifted so that the position of their centre of mass does not change

Answer 1

Answer:

15cm

Explanation:

M1 = 10kg & M2 = 30kg

position of M1 = x1 cm

position of M2 = x2 cm

position of CM : x = {10(x2) + 30(x1)}/(10+30) = {10(x2) + 30(x1)}/40

new position of x1 : x'1 = (x1 + 5) cm

new position of x2 : x'2 = (x2-k) cm

new position of CM : x' = {10(x'2) + 30(x'1)}/(10+30) = {10(x2-k) + 30(x1+5)}/40 = 10(x2) + 30(x1)}/(10+30) = x + (150 - 10k)/40

but x = x'...and hence....

x = x + (150 - 10k)/40

(150 - 10k)/40 = 0

therefore ...k = 15cm