Question

In the sonometer experiment, a tuning fork of frequency $256Hz$ is in resonance with $0.4m$ length of the wire when the iron load attached to free end of wire is $2kg$. 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)

For a sonometer
$v=\frac{1}{2l}\sqrt{\frac{T}{\mu }}$
$256=\frac{1}{2(0.4m)}\sqrt{\frac{2g}{\mu }}$
Weight of iron $=V\rho g=V8g=2g$
$\Rightarrow V=\left(\frac{1}{4}\right)$
Apparent weight of iron in water $=V(\rho -\sigma )g$
$=V(8-1)g=V7g=\frac{7}{4}g$
$\Rightarrow \frac{1}{2l^{\prime }}\sqrt{\frac{\frac{7}{4}g}{\mu }}=\frac{1}{2(0.4)}\sqrt{\frac{2g}{\mu }}$
or $l^{\prime }=(0.4)\sqrt{\frac{7}{8}}=0.37m$