Question

A light string passing over a smooth light pulley connects two blocks of masses m₁ and m₂ (vertically). If the acceleration of the system is g/8, then the ratio of the masses is:

(1) 8: 1 

(2) 9: 7 

(3) 4: 3 

(4) 5: 3

Answer 1

(2) The ratio of the masses is 9 : 7.

Explanation:

Since the string is inextensible, therefore both the masses will have same acceleration a. Also, the string is frictionless and massless therefore it will have same tension at both the ends.  

Suppose m₂ is greater then m₁ which means m₂ is coming down and m₁ is going up.  

Using Newton's Second Law of motion on the block of mass m₁  

T - m₁g = m₁a  

Again, applying the second law on the block of mass m₂  

m₂g - T = m₂a  

Given that a = g/8 or g = 8a  

8m₂a - T = m₂a  

T = 7m₂a  

Substitute this value of T in the first equation  

7m₂a - 8m₁a = m₁a  

7m₂ = 9m₁