The string vibrates in 4 loops when a $50\text{ g}$ weight is placed in the pan of weight $15\text{ g}$. To…
The string vibrates in 4 loops when a $50\text{ g}$ weight is placed in the pan of weight $15\text{ g}$. To make the string to vibrate in 6 loops the weight that has to be removed from the pan is
(a) $0.0007\text{ kg-wt}$
(b) $0.0021\text{ kg-wt}$
(c) $0.036\text{ kg-wt}$
(d) $0.0029\text{ kg-wt}$
Solution
Frequency of vibration of string is given by
$n = \frac{1}{2l} \sqrt{\frac{T}{m}} \Rightarrow P\sqrt{T} = \text{constant}$
where, $P$ is number of loops formed.
$\frac{P_1}{P_2} = \sqrt{\frac{T_2}{T_1}}$
Hence, $\frac{4}{6} = \sqrt{\frac{T_2}{(50 + 15)}} \Rightarrow T_2 = 28.8\text{ gf}$
Hence, weight to be removed from the pan
$= T_1 - T_2 = 65 - 28.8 = 36.2\text{ g force}$
$= 0.036\text{ kg-wt}$