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Q.

A block is lying on the horizontal frictionless surface. One end of a uniform rope is fixed to the block which is pulled in the horizontal direction by applying a force F at the other end. If the mass of the rope is half the mass of the block, the tension in the middle of the rope will be

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a

F

b

2F/3

c

3F/5

d

5F/6

answer is D.

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Detailed Solution

The acceleration of block-rope system is a=F(M+m),where M is the mass of block and m is the mass of rope. So the tension in the middle of the rope will be T={M+(m/2)}a=M+(m/2)FM+m. Given that m = M/2, T=M+(M/4)M+(M/2)F=5F6
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