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Question

# A frictionless cart A of mass 100 kg carries other two frictionless carts B and C having masses 8kg and 4kg respectively connected by a string passing over a pulley as shown in figure. What horizontal force F must be applied on the cart so that smaller carts do not move relative to it ?

A
560 N
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B
150 N
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C
630 N
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D
340 N
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Solution

## The correct option is A 560 NLet a be the acceleration of the system in the right direction.Since the smaller carts do not move relative to the larger one, the equation of motion of the whole system,(mA+mB+mC)a=F(100+8+4)a=F ⟹F=112aAs block B experience a pseudo force which is equal to ma and as the blocks are at rest so this psudo force balance the T.For block B, T=mBa=8a ....(1)Block C is not moving so we balance the forces in vertical direction.For block C, T=4g ....(2)From (1) and (2), we get 8a=4gThus a=0.5g a=5m/s2 (as g=10m/s2)∴F=112×5=560 N

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