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Question

An angular structure ABC with side AB=BC=L is made up of two thin rods AB of mass m and BC of mass 2m. The structure when hanged from point A stays in equilibrium with side BC horizontal. Find the value of angle θ.


A
30
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B
cos1(25)
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C
sin1(35)
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D
π2sin1(35)
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Solution

The correct option is B cos1(25)

For equilibrium, the net torque about point A should be zero.

Now, the torque due mass m and 2m about A are,

τm=mgL2cosθ

τ2m=2mg(L2Lcosθ)

For equilibrium,

τmg=τ2mg

mgL2cosθ=2mg(L2Lcosθ)

52cosθ=1

θ=cos1(25)

Hence, option (B) is the correct answer.

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