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Physics-

General

Easy

Question

A massless rod is suspended by two identical strings AB and CD of equal length. A block of mass m is suspended from point O such that $B O$ is equal to $´ ´ x ´ ´$ Further, it is observed that the frequency of 1^st harmonic (fundamental frequency) in AB is equal to 2^nd harmonic frequency in CD. Then, length of BO is

$\frac{L}{5}$
$\frac{4 L}{5}$
$\frac{3 L}{4}$
$\frac{L}{4}$

The correct answer is: $fraction numerator L over denominator 5 end fraction$

According to question,

$fraction numerator 1 over denominator 2 l end fraction square root of fraction numerator T subscript 1 end subscript over denominator mu end fraction end root equals fraction numerator 1 over denominator l end fraction square root of fraction numerator T subscript 2 end subscript over denominator mu end fraction end root$
$T subscript 2 end subscript equals T subscript 1 end subscript divided by 4$
For rotational equilibrium,
$T subscript 1 end subscript x equals T subscript 2 end subscript open parentheses L minus x close parentheses rightwards double arrow x minus L divided by 5$

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