Question

Two spherical bob of masses $M_A$ and $M_B$ are hung vertically from two strings of length $l_A$ and $l_b$ respectively. They are executing SHM with frequency relation $f_A=2f_B$, Then :

• A. ${\ell }_A=\frac{{\ell }_B}{4}$
• B. ${\ell }_A=\frac{{\ell }_B}{4}$
• C. ${\ell }_A=2{\ell }_B\&M_A=2M_B$
• D. ${\ell }_A=\frac{{\ell }_B}{2}\&M_A=\frac{M_B}{2}$

Answer 1

The correct option is B ${\ell }_A=\frac{{\ell }_B}{4}$

$f=\frac{1}{2\pi }\sqrt{\frac{g}{\ell }}$

$f\propto \frac{1}{\sqrt{\ell }}$

$\frac{f_A}{f_B}=\sqrt{\frac{{\ell }_B}{{\ell }_A}}$

$⟹\frac{2f_B}{f_B}=\sqrt{\frac{{\ell }_B}{{\ell }_A}}$

$⟹4=\frac{{\ell }_B}{{\ell }_A}$

$⟹{\ell }_A=\frac{{\ell }_B}{4}$