Question

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. $l_{A}=\frac{l_{B}}{4}$, does not depend on mass
• B. $l_{A}=4 l_{B}$, does not depend on mass
• C. $l_{A}=2 l_{B}$ and $M_{A}=2 M_{B}$
• D. $l_{A}=\frac{l_{B}}{2}$ and $M_{A}=\frac{M_{B}}{2}$.

Answer 1

Answer: (A)

$f_{A}=2 f_{B}$
$\Rightarrow \frac{1}{2 \pi} \sqrt{\frac{g}{l_{A}}}=2 \times \frac{1}{2 \pi} \sqrt{\frac{g}{l_{B}}}$
or, $\frac{1}{l_{A}}=4 \times \frac{1}{l_{B}}$.
or, $l_{A}=\frac{l_{B}}{4}$,
which does not depend on mass.