Question

In Searle's method to find Young's modulus of a wire, when a force of $1.5$ kg-wt is applied at its free end, the length of wire is $a$. When force of $2.5$ kg-wt is applied, the length of wire is $b$. What would be its original length?

• A. $b - a$
• B. $\dfrac{b - a}{4}$
• C. $2.5a - 1.5b$
• D. $2.5b - 1.5a$

Hint:

Always express extensions using proportionality before eliminating constants.

Answer 1

The Correct Option is C

Step 1: Use linear relation of extension.
Extension in a wire is directly proportional to the applied force.

Step 2: Express lengths mathematically.
Let original length be $L$.
\[ a = L + k(1.5) \] \[ b = L + k(2.5) \]

Step 3: Eliminate constant $k$.
\[ b - a = k(2.5 - 1.5) = k \]

Step 4: Substitute to find $L$.
\[ L = a - 1.5k = a - 1.5(b - a) \] \[ L = 2.5a - 1.5b \]

Step 5: Conclusion.
The original length of the wire is $2.5a - 1.5b$.