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Question

A rope of mass m is attached to a block of mass M lying on a horizontal surface. The block is pulled along the surface by applying a force F on the free end of the rope. If μ is the coefficient of friction between block and the surface, the force exerted by the rope on the block is


A
m(M+m)(Fμmg)
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B
M(M+m)(FμMg) 
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C
mM(F+μmg)
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D
M(m+M)(F+μMg)
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Solution

The correct option is D M(m+M)(F+μMg)
The free-body diagrams of the block and the rope are shown in Fig.

For block : Tf=Ma where f=μMg
TμMg=Ma.........(1)
For rope:
FT=ma........(2)
Dividing (1) by (2) and simplifying,
TμMgFT=Mm
TμMg=MmFTMm
T[1+Mm]=Mm[F+μmg]
T=M(M+m)[F+μmg]
we find that the correct choice is (d).

Physics

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