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Question

In the following figures (i) and (ii), all the surfaces are smooth, string is massless and pulley is ideal. The mass of rope is m in both the cases. If T1 and T2 be the tensions at the mid points of the ropes in figure (i) and figure (ii) respectively, then T1:T2 is

A
m:M
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B
m:(M+m)
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C
(M+m):m
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D
1:1
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Solution

The correct option is A m:(M+m)

Case I
T=ma
MgT=Ma
Mg=(M+m)a
a=Mg(M+m)
T=ma=Mm(M+m)×g
T1=m2×M(M+m)×g

Case II
Now a2=Mmg
T2=m2×Mmg
T1:T2=1(M+m):1m=m:(M+m)

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