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Q.

A T shaped rod is hinged at it's corner as shown and free to rotate in a vertical plane. The rods have mass m each and length L each. Find angle $θ$ made by upper end in the equilibrium

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a

$\tan^{- 1} (\frac{1}{2})$

b

$\tan^{- 1} (2)$

c

$37 °$

d

$53 °$

answer is B.

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Detailed Solution

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Centre of mass is vertically below the hinge. Center of mass of the system at a distance l/4 from the junction on the vertical rod
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$\tan (90 ° - θ) = \frac{\frac{l}{4}}{\frac{l}{2}} = \frac{1}{2} \Rightarrow \tan θ = 2$

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A T shaped rod is hinged at it's corner as shown and free to rotate in a vertical plane. The rods have mass m each and length L each. Find angle θ made by upper end in the equilibrium