Question

In Melde’s experiment, when the tension decreases by \(0.009\,\text{kg-wt}\), the number of loops changes from 4 to 5. The initial tension is

• A. \(0.036\,\text{kg-wt}\)
• B. \(0.009\,\text{kg-wt}\)
• C. \(0.018\,\text{kg-wt}\)
• D. \(0.025\,\text{kg-wt}\)

Hint:

In Melde’s experiment, number of loops varies inversely as square root of tension.

Answer 1

The Correct Option is D

Step 1: Relation between tension and number of loops.
In Melde’s experiment, \[ T \propto \frac{1}{n^2} \]

Step 2: Write ratio of tensions.
Let initial tension be \(T_1\) for 4 loops and final tension be \(T_2\) for 5 loops.
\[ \frac{T_1}{T_2} = \left(\frac{5}{4}\right)^2 = \frac{25}{16} \]

Step 3: Use given decrease in tension.
\[ T_1 - T_2 = 0.009 \]
Solving these equations, \[ T_1 = 0.025\,\text{kg-wt} \]