A uniform rod of length 4L and mass M is suspended form a horizontal roof by two light strings of length L and 2L as shown. Then the tension in the left string of length L is:
Mg2
Mg3
35Mg
Mg4
A
Mg2
B
35Mg
C
Mg4
D
Mg3
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Solution
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AC=4L BC=L AB=√AC2−BC2 =√(4L)2−L2 =√16L2−L2 =√15L2 AB=√15L Also, cosθ=ABAC=AEAD =√15L4L=AE2L AE=√154×2L AE=√152L taking moment at A T1×AB=Mg×AE T1×√15L=Mg×√152L T1=Mg2
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