An inextensible string passing over a smooth pulley connects two blocks of masses m₁ and m₂ ( m₂ > m₁ ) vertically. If the acceleration of the system is ( g n ) , then the ratio of masses ( m₂ m₁ ) is

Step-by-step solution

For an Atwood machine with masses m₁ and m₂ ( m₂ > m₁ ), the acceleration a is given by: a = m₂ - m₁ m₂ + m₁ g Given that a = g n , we can write: m₂ - m₁ m₂ + m₁ g = g n m₂ - m₁ m₂ + m₁ = 1 n Dividing the numerator and denominator of the left side by m₁ : m₂ m₁ - 1 m₂ m₁ + 1 = 1 n Cross-multiplying yields: n ( m₂ m₁ - 1 ) = m₂ m₁ + 1 n m₂ m₁ - n = m₂ m₁ + 1 m₂ m₁ (n - 1) = n + 1 m₂ m₁ = n + 1 n - 1 Answer: n+1 n-1