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  4. In Melde's experiment, the string vibrates in 4 loops when a 50 g weight is placed in the pan of weight 15 g. To make the strings to vibrates in 6 Joops the weight that has to be removed from the pan is

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Q. In Melde's experiment, the string vibrates in $4$ loops when a $50\, g$ weight is placed in the pan of weight $15\, g$. To make the strings to vibrates in $6$ Joops the weight that has to be removed from the pan is

MHT CETMHT CET 2004Electromagnetic Waves

Solution:

The transverse vibrations of a string are determined by Melde's method.
The frequency of vibration of a string of length $l$, mass per unit length m and vibrating in $p$ loops under tension $T$ is given by
$n_= \frac{P}{2l} \sqrt{\frac{T}{m}} $
or $p \sqrt T$ = constant
If $n, l$ and m are constant.
Hence, $T \propto \frac{1}{p^2} $
$\therefore \frac{T_1}{T_2} = \frac{p^2_2}{p^2_1}$
or $\frac{(50+15)}{T_2} = \frac{(6)^2}{(4)^2}$
or $\frac{65}{T_2} = \frac{36}{16}$
$\therefore T_2 = \frac{65 \times 16 }{36} = 29g$
So, weight removed from the pan
$= 65 - 29 = 36g$
$= 0.036\, kg-wt $