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Question

Two identical thin rods each with mass m and length L are joined at right angles to form an L-shpaed object This object is balanced on top of a sharp edge as shown in the figure if the L-shaped object is deflected slightly it oscillates The frequency of oscillation is
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A
12π3g2L
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B
12π3g42L
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C
12π3g22L
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D
12π3gL
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Solution

The correct option is B 12π3g22L
If L- shaped object is slightly displaced by an angle θthen
τ0=mgL2{sin(45θ)sin(45+θ}=mgL2{22sinθ}
2(mL23)α=mgL2θ
α=3g22Lθ
ω=3g22L

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