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A rod PQ of length 'L' is hung from two identical wires A and B. A block of mass 'm' is hung at point R of the rod as shown in figure. The value of 'x' so that the fundamental mode in wire A is in resonance with first overtone of B is ___`

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4L/5

2L/3

L/5

L/4

answer is C.

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Detailed Solution

torque equation about the point R
$T_{1} x = T_{2} (L - x)$

$and, \frac{1}{2 l} \sqrt{\frac{T_{1}}{μ}} = \frac{2}{2 l} \sqrt{\frac{T_{2}}{μ}}$

$\Rightarrow T_{1} = 4 T_{2}$

$∴ 4 T_{2} x = T_{2} (L - x)$

$\Rightarrow 4 x = L - x \Rightarrow 5 x = L \Rightarrow x = \frac{L}{5}$

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