Question

In Melde's experiment, it was found that the string vibrates in $5$ loops. When $10gms$ are placed in a light pan. What weight must be placed to the pan to make it vibrates in $10$ loops? Neglect the weight of the pan.

• A. $2.5gm$
• B. $5gm$
• C. $7.5gm$
• D. $12.5gm$

Answer 1

The correct option is A $2.5gm$

When a string of linear density '$m$', under tension '$T$', vibrates in '$n$' loops, the frequency, $\frac{n}{2l}\sqrt{\frac{T}{m}}=N$

$T{n}^2=4l^2{N}^{2}m=constant$

$T_1{n}_1^2=T_2{n}_2^2\Rightarrow T_2=\frac{n_1^2}{n_2^1}\times T_1=\frac{5^2}{{10}^2}\times 10=2.5gm$