Question

An iron load of $2kg$ is suspended in air from the free end of a sonometer wire of length one meter. A tuning fork of frequency $256Hz$ is in resonance with $1/\sqrt{7}$ times the length of the sonometer wire. If the load is immersed in water, the length of the wire in meter that will be in resonance with the same tuning fork is :

(Specific gravity of iron $=8$)

• A. $\sqrt{8}$
• B. $\sqrt{6}$
• C. $\frac{1}{\sqrt{6}}$
• D. $\frac{1}{\sqrt{8}}$

Answer 1

Answer: (D)

$\frac{1}{\sqrt{8}}$

$f\propto \frac{1}{l}\sqrt{\frac{T}{\mu }}$
$\Rightarrow l\propto \sqrt{T}$
$\therefore \frac{l_1}{l_2}=\sqrt{\frac{T_1}{T_2}}=\sqrt{\frac{8}{7}}$
$\frac{1}{\sqrt{7}{l}_2}=\frac{\sqrt{8}}{\sqrt{7}}$
$\Rightarrow l_2=\frac{1}{\sqrt{8}}$