JEE Main · PhysicsHard

$Two blocks of masses m_{1} and m_{2} are connected by a light string passing over a pulley of mass M and radius R . The pulley is a uniform disk. If the system is released from rest, what is the acceleration of the blocks?$

Show correct answer & step-by-step solution

Correct answer: A — $\frac{( m _{2} - m _{1} ) g}{m _{1} + m _{2} + M /2}$

Solution

Applying Newton's second law to the blocks: T_{2} - m_{2} g = - m_{2} a and T_{1} - m_{1} g = m_{1} a . For the pulley, (T_{2} - T_{1}) R = I α = (\frac{1}{2} M R^{2}) (\frac{a}{R}) . Solving these equations simultaneously gives a = \frac{( m _{2} - m _{1} ) g}{m _{1} + m _{2} + M /2} .