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Question

# In the following figure the masses of the blocks A and B are the same and each equal to m. The tensions in the strings OA and AB are T2 and T1 respectively. The system is in equilibrium with a constant horizontal force mg on B. Then T2 is:

A
mg
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B
2mg
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C
3mg
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D
5mg
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Solution

## The correct option is D √5mgFrom the free body diagram of block B: T1cosθ1=mg(i) T1sinθ1=mg(ii) By squaring and adding T21(sin2θ1+cos2θ1)=2(mg)2 ∴T1=√2mg also θ1=45° From the free body diagram of block A For vertical equilibrium T2cosθ2=mg+T1cosθ1 T2cosθ2=mg+√2mgcos45o or T2cosθ2=2mg(i) For horizontal equilibrium T2sinθ2=T1sinθ1=√2mgsin45o T2sinθ2=mg(ii) By squaring and adding (i) and (ii) equilibrium: T22=5(mg)2 or T2=√5mg

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