Two masses M_{A} and M_{B} are hung from two strings of length l_{A} and l_{B} respectively. They ar

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13.Oscillations

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Two masses $M_{A}$ and $M_{B}$ are hung from two strings of length $l_{A}$ and $l_{B}$ respectively. They are executing SHM with frequency relation $f_{A}=2 f_{B}$, then relation

A

$l_{A}=4 l_{B},$ does not depend on mass

B

$l_{A}=\frac{l_{B}}{4},$ does not depend on mass

C

$l_A=2 l_B$ and $M_A=2M_B$

D

$l_{A}=\frac{l_{B}}{2}$ and $M_{A}=\frac{M_{B}}{2}$

(AIPMT-2000)

Solution

$f_{A}=2 f_{B}$

$\Rightarrow \frac{1}{2 \pi} \sqrt{\frac{g}{l_{A}}}=2 \times \frac{1}{2 \pi} \sqrt{\frac{g}{l_{B}}} $

$\quad \frac{1}{l_{A}}=4 \times \frac{1}{l_{B}}$

or, $l_{A}=\frac{l_{B}}{4},$ which does not depend on mass.

Standard 11

Physics

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