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Question

In the figure given below, two blocks of mass m and M are connected through a light inextensible rope. Then, find the tension in the connecting rope. Consider coefficient of static friction between the inclined surface and the blocks to be μ.


A
(M+m)gsinθ
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B
(M+m)gsinθμmgcosθ
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C
Zero
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D
(M+m)gcosθ
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Solution

The correct option is C Zero
From FBD:


Applying equilibrium condition perpendicular to the inclined surface
N1=Mgcosθ &
N2=mgcosθ

Let us assume that both blocks move with acceleration a down the incline to maintain the string constraint.
For block M, equation of dynamics is:
Ma=MgsinθTf1
where f1=μN1=μMgcosθ (kinetic friction)
Ma=MgsinθTμMgcosθ
a=gsinθTMμgcosθ....(i)

For block m, equation of dynamics is:
ma=mgsinθ+Tf2
where f2=μN2=μmgcosθ
ma=mgsinθ+Tμmgcosθ
a=gsinθ+Tmμgcosθ....(ii)

Equating Eq. (i) and (ii):
gsinθTMμgcosθ=gsinθ+Tmμgcosθ
TM+Tm=0 ....(iii)
Since mass can never be zero for the blocks, for validating Eq. (iii)
T=0
option (C) is correct.

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