Two identical blocks each of mass ' M ' attached to the ends of a massless inextensible string which passes over a pulley with a fixed axis as shown below. A small mass ' m ' is no

Question

Two identical blocks each of mass ' M ' attached to the ends of a massless inextensible string which passes over a pulley with a fixed axis as shown below. A small mass ' m ' is now placed on the block B. The acceleration with which the two blocks move together is [ g = gravitational acceleration]

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Let T be the tension in the string and a be the common acceleration of the system. The total mass on the right side is M + m and it moves downwards. The equation of motion is: ( M + m ) g − T = ( M + m ) a The total mass on the left side is M and it moves upwards. The equation of motion is: T − M g = M a Adding the two equations, we get: ( M + m ) g − M g = ( M + m ) a + M a m g = ( 2 M + m ) a a = 2 M + m m g ​ Answer: 2 M + m mg ​

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