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

Solution

Physics sir · 4 steps

The weight difference drives both blocks, so set (m₁ - m₂)/(m₁ + m₂) = 1/8.

1. Treat as one system. The string is light and the pulley is smooth, so both blocks share one acceleration and the tension is internal. Take m₁ as the heavier block. The net driving force is (m₁ - m₂)g, and it accelerates the total mass m₁ + m₂.

   a = ((m₁ - m₂) g)/(m₁ + m₂) = g/8

2. Solve for the ratio. Cross-multiply: 8(m₁ - m₂) = m₁ + m₂, so 7m₁ = 9m₂. This gives m₁/m₂ = 9/7.
3. Check. (9 - 7)/(9 + 7) = 2/16 = 1/8, which matches a = g/8.
4. So. The ratio of masses is 9/7, option (b).

The idea to keep. For an Atwood machine, a/g = (m₁ - m₂)/(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.