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Question

In figure both the pulleys are massless and frictionless. A force F (of any possible magnitude) is applied in horizontal direction. There is no friction between M and the ground. μ1 and μ2 are coefficients of friction as shown between the blocks. Column I gives the different relations between μ1 and  μ2 and Column II is regarding the motion of M. Match the columns.


Column IColumn IIi. If μ1=μ2=0a. may accelerate towards rightii. If μ1=μ20b. may accelerate towards leftiii. If μ1>μ2c. does not accelerateiv. If μ1<μ2d. may or may not accelerate
 


A
(i- c; ii- c; iii- b, d; iv- a, d)
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B
(i-c; ii- b; iii- c, d; iv- a, d)
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C
(i- b,d; ii- c; iii- b, d; iv- a, d)
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D
(i- a,c; ii- c; iii-  d; iv-  d)
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Solution

The correct option is A (i- c; ii- c; iii- b, d; iv- a, d)
Friction force and tension acting between blocks and string are shown below,

F.B.D of lower block is,
So the movement of lower block depend on the value of μ1 and μ2.
If μ1=μ2=0, then f1 and f2 are also zero. Hence the block does not accelerate.
If μ1=μ2, then f1=f2 . In this case also the block does not accelerate.
If μ1>μ2,
Both kinetic and static friction come into picture, and we can say,
(1) Limiting friction on block in L.H.S R.H.S.
(2) Limiting friction in R.H.S kinetic friction in L.H.S of block.
(3) Kinetic friction in R.H.S of block is greater than L.H.S side of block.
From here we can conclude that
Block may accelerate towards left or may or may not accelerate.
Similarly, if μ1<μ2 , we can conclude that block may accelerate towards right or  may or may not accelerate.

Physics

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