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A massless rod $B D$ is suspended by two identical massless string $A B$ and $C D$ of equal lengths. A block of mass $m$ is suspended from point $P$ such that $B P$ is equal to $x$ . If the fundamental frequency of the left wire is twice the fundamental frequency of right wire, then the value of $x$ is

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$x = 3 l / 4$

$x = l / 5$

$x = 4 l / 5$

$x = l / 4$

answer is A.

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Detailed Solution

$f \propto v \propto \sqrt{T} \Rightarrow f_{A B} = 2 f (D)$

$∴$ $T_{A8} = 4 T_{CD}$

Further

$Σ τ_{p} = 0$

$∴$ $T_{A B} (x) = T_{C D} (l - x)$

$4 x = l - x$

(as $T_{A B} = 4 T_{C}$ )

$x = l / 5$

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