Question

In the sonometer experiment, a tuning fork of frequency 256 Hz is in resonance with 0.4m length of the wire when the iron load attached to free end of the wire is 2 kg. If the load is immersed in water, the length of the wire in resonance would be (specific gravity of iron=8)

• A. 0.37 m
• B. 0.43 m
• C. 0.31 m
• D. 0.2 m

Answer 1

Answer: (A)

0.37 m

The tension in the string initially $=mg=Vdg$

where, $m=2kg$

Tension after immersion in water $=mg-V\rho g=Vdg-V\rho g$ $=Vd(1-\frac{\rho }{d})g$ $=mg(1-\frac{\rho }{8})=\frac{7}{8}mg$

Since the frequency remains the same,

$\frac{\sqrt{T_1}}{l_1}=\frac{\sqrt{T_2}}{l_2}$
$⟹\frac{\sqrt{mg}}{0.4}=\frac{\sqrt{\frac{7}{8}mg}}{l_2}$

$⟹l_2=0.37m$