Question

A wire is attached to a pan of mass 200 g that contains a 2.0 kg mass, as shown in the figure. When plucked, the wire vibrates at a fundamental frequency of 220 Hz. An additional unknown mass M is then added to the pan and a fundamental frequency of 260 Hz is detected. The value of M is $873\times {10}^{-x}kg$. Find x.

• A. 3
• B. 2
• C. 1
• D. 6

Answer 1

The correct option is A 3

Fundamental frequency of oscillation of the string=$\frac{1}{2l}\sqrt{\frac{T}{\mu }}$

Initially tension in the string=$T_1=2.2g$

Finally tension in the string=$T_2=(2.2+M)g$

Thus $\frac{f_2}{f_1}=\sqrt{\frac{T_2}{T_1}}$

$⟹\sqrt{\frac{2.2+M}{2.2}}=\frac{260}{220}$

$⟹M=0.873kg$