Q. An iron load of 2 kg is suspended in air from the free end of a sonometer wire of length 1m. A tuning fork of frequency 256 Hz is in resonance with $1/\sqrt{7\ }\ $ time the length of the sonometer wire. If the load is immersed in metre that will be in resonance with the same tuning fork is (specified gravity of iron=8)
A) $\sqrt{8}$
B) $\sqrt{6}$
C) $\frac{1}{\sqrt{6}}$
D) $\frac{1}{\sqrt{8}}$
Explanation
(d) We know $l \propto \sqrt{T}$
$\therefore\frac{\iota_{air}}{\iota_{water}} = \sqrt{\frac{T_{air}}{T_{water}}}\ $
But specific gravity 8=
$\frac{T_{air}}{T_{air} - T_{water}}$
$\Longrightarrow T_{water} = \frac{7}{8}T_{air}\ $
$\therefore\ \frac{l_{air}}{l_{water}} = \sqrt{\frac{8}{7}}$
But
$l_{air} = \frac{1}{\sqrt{7}}l\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (Given)$
$\therefore\ \ \ l_{water} = \frac{1}{\sqrt{8}}l$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.