The mass of the body which is hanging on the rope attached to the movable pulley is four times as much as the mass of the body which is fixed to the ground. At a given instant the fixed body is releas

Question

The mass of the body which is hanging on the rope attached to the movable pulley is four times as much as the mass of the body which is fixed to the ground. At a given instant the fixed body is released. What is its initial acceleration (in $m / s^{2}$ )? (The mass of the pulleys and the ropes is negligible.)

$(m / s^{2})$

TestHub · Accepted Answer

For the released mass m : T − m g = ma For the 4 m mass on the movable pulley: 4 m g − 2 T = 4 m a ′ , with constraint a ′ = 2 a ​ Substituting T = m ( g + a ) : 4 m g − 2 m ( g + a ) = 2 ma a = 2 g ​ = 5 m/s 2

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