Question

When tension of a string is increased by 2.5 N, the initial frequency is altered in the ratio of 3:2. The initial tension in the string is

• A. 6 N
• B. 5 N
• C. 4 N
• D. 2 N

Answer 1

The correct option is D 2 N

Let initial tension = T.
Then given that:
$2\nu =\sqrt{\frac{T}{\mu }}$ $2\nu$ is the frequency
Upon increasing the tension by 2.5N, the frequency becomes $3\nu$
$3\nu =\sqrt{\frac{T+2.5}{\mu }}$
Dividing the two equations.
$\frac{3}{2}=\sqrt{\frac{T+2.5}{T}}$
$\frac{9}{4}=\frac{T+2.5}{T}$
$9T=4T+10$
$5T=10$
$T=2N$
Option d is correct.