Consider the setup illustrated in the figure. The applied force F is equal to m₂ g/2 . Assuming the string is light and there is no friction present anywhere, determine the strain developed in the string if its cross-sectional area is A and its Young modulus is Y .

Step-by-step solution

Let a be the acceleration of the system and T be the tension in the string. Assuming the block of mass m₂ moves downwards and m₁ moves to the right, the equations of motion are: For mass m₂ : m₂ g - T = m₂ a For mass m₁ : T - F = m₁ a Adding the two equations, we get: m₂ g - F = (m₁ + m₂) a Given that F = m₂ g 2 , substituting this into the equation: m₂ g - m₂ g 2 = (m₁ + m₂) a m₂ g 2 = (m₁ + m₂) a a = m₂ g 2(m₁ + m₂) Now, substituting the value of a in the equation for m₂ to find the tension T : T = m₂ g - m₂ a T