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  4. A massless rod BD of length l is suspended by two identical massless strings AB and CD of equal lengths. A block of mass m is suspended from a point P such that BP is equal to x . If the fundamental frequency of the left wire is twice the fundamental frequency of the right wire, then the value of (l/x) is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-hbrkyjv9kf8ziklm.jpg />

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Q. A massless rod $BD$ of length $l$ is suspended by two identical massless strings $AB$ and $CD$ of equal lengths. A block of mass $m$ is suspended from a point $P$ such that $BP$ is equal to $x$ . If the fundamental frequency of the left wire is twice the fundamental frequency of the right wire, then the value of $\frac{l}{x}$ is
Question

NTA AbhyasNTA Abhyas 2022

Solution:

$f \propto v \propto \sqrt{T}$
$f_{ AB }=2 f_{ CD }$
$\therefore T _{ AB }=4 T _{ CD } \ldots$ (i)
Further $\Sigma \tau_{ p }=0$
$\therefore( T )_{ AB }(x)=( T )_{ CD }(\ell-x)$
or $4 x =l- x \left(( T )_{ AB }=4( T )_{ CD }\right)$
or $x =l / 5$
$\Rightarrow \frac{l}{x}=5$