Q. In a sonometer wire, the tension is maintained by suspending a $50.7\ kg$ mass from the free end of the wire. The suspended mass has a volume of $0.0075\ m^{3}.$ The fundamental frequency of the wire is $260\ Hz.$ If the suspended mass is completely submerged in water, the fundamental frequency will become (take $g = 10\ ms^{- 2}$)
A) $240\ Hz$
B) $230\ Hz$
C) $220\ Hz$
D) $200\ Hz$
Explanation
(a) $n = \frac{\rho}{2l}\sqrt{\frac{T}{m}} \propto \sqrt{T} \Rightarrow \frac{n_{1}}{n_{2}} = \sqrt{\frac{T_{1}}{T_{2}}}$
$\Rightarrow \frac{260}{n_{2}} = \sqrt{\frac{50.7g}{(50.7 - 0.0075 \times 10^{3})g}} \Rightarrow n_{2} = 240$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.