Question

The amount of work done in stretching a spring from a stretched length of 10 cm to a stretched length of 20 cm is-

• A. Equal to the work done in stretching it from 20 cm to 30 cm
• B. Less than the work done in stretching it from 20 cm to 30 cm.
• C. More than the work done in stretching it from 20 cm to 30 cm.
• D. Equal to the work done in stretching it from 0 to 10 cm.

Answer 1

The correct option is B Less than the work done in stretching it from 20 cm to 30 cm.

Work done in stretching a spring to x length is $W=\frac{1}{2}k{x}^2$
$\therefore$ Work one in stretching from $x_1$ to $x_2$ is proportional to $W\propto x_2^2-x_1^2$
hence $\frac{W_{20,30}}{W_{10,20}}=\frac{500}{300}$
so, 10 to 20 takes less work when compared to 20 to 30.