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

Solution

Physics sir · 4 steps

Net pull over total mass gives the acceleration. Set that equal to g/8 and the ratio drops out.

1. Treat as one system. Take m₂ as the heavier block. The string tension is internal, so the only net driving force is the difference in weights, (m₂ - m₁)g. It moves the total mass m₁ + m₂.

   a = ((m₂ - m₁) g)/(m₁ + m₂) = g/8

2. Solve for ratio. Cross-multiply: 8(m₂ - m₁) = m₁ + m₂. This gives 8m₂ - m₂ = 8m₁ + m₁, so 7m₂ = 9m₁.
3. Check. With m₂ = 9 and m₁ = 7, the acceleration is a = (9-7)g/16 = 2g/16 = g/8, as required.
4. So. m₂/m₁ = 9/7, that is 9 : 7, option (c).

The idea to keep. For two blocks over an ideal pulley, a = (m₂ - m₁)g/(m₁ + m₂). If a = g/n, the masses are in the ratio (n+1) : (n-1).

Answer from the NTA final answer key. Solution by PrepWiser.