Laws of Motion

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. 5:3
  2. 4:3
  3. 8:1
  4. 9:7

Solution

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 firs equation

7m2a - 8m1a = m1a

7m2 = 9m1

The correct option is D.