Question

When a wire of length $L$ clamped at one end is pulled by a force $F$ from the other end, its length increases by $L'$. If the radius and the applied force are halved, then the increase in its length is

• A. $3L$
• B. $4L$
• C. $1.5L$
• D. $2L$

Hint:

Extension $\Delta L$ is directly proportional to $F$ and inversely proportional to area $A$.

Answer 1

The Correct Option is D

Extension in a wire: $\Delta L = \dfrac{FL}{AY}$
Radius halved $\Rightarrow$ Area becomes $\dfrac{1}{4}A$
Force halved $\Rightarrow$ $F' = \dfrac{F}{2}$
New extension: $\Delta L' = \dfrac{(F/2)L}{(A/4)Y} = \dfrac{F L}{2} \cdot \dfrac{4}{A Y} = 2 \cdot \dfrac{F L}{A Y} = 2L$