Question

Two wires are stretched through same distance. The force constant of second wire is half as that of the first wire. The ratio of work done to stretch first wire and second wire will be

• A. $2:1$
• B. $1:2$
• C. $3:1$
• D. $1:3$

Answer 1

The correct option is A $2:1$

As $W=\frac{1}{2}k{x}^2$
If both wires are stretched through same distance, then $W\propto k$
It is given that $k_2=\frac{k_1}{2}$
$\therefore \frac{W_1}{W_2}=\frac{k_1}{k_2}$
$=\frac{k_1}{\frac{k_1}{2}}=\frac{2}{1}=2:1$