Two blocks of masses m₁ and m₂ (where m₁ > m₂ ) are connected by a light inextensible string that passes over a frictionless pulley. If the acceleration of the system is g 2 , what is the ratio of their masses ( m₁ : m₂ )?

Step-by-step solution

For an Atwood machine with masses m₁ and m₂ ( m₁ > m₂ ), the acceleration a is given by: a = m₁ - m₂ m₁ + m₂ g Given that a = g 2 , we can write: g 2 = m₁ - m₂ m₁ + m₂ g Cancelling g from both sides: 1 2 = m₁ - m₂ m₁ + m₂ Cross-multiplying yields: m₁ + m₂ = 2m₁ - 2m₂ Rearranging the terms: 3m₂ = m₁ m₁ m₂ = 3 1 Thus, the ratio m₁ : m₂ is 3 : 1 . Answer: 3 : 1