Question

Two springs of force constants $K_1$ and $K_2$ $(K_1>K_2)$ are stretched by same force. If $W_1$ and $W_2$ be the work done stretching the springs then

• A. $W_1=W_2$
• B. $W_1<W_2$
• C. $W_1>W_2$
• D. $W_1=W_2=0$

Answer 1

The correct option is B $W_1<W_2$

As the force on both the springs is same, we have

$F=k_1{x}_1=k_2{x}_2$ .....(1)

Now, work done on first spring, $W_1=\frac{1}{2}{k}_1{x}_1^2$ .......(2)

Work done on second spring, $W_2=\frac{1}{2}{k}_2{x}_2^2$ ...(3)

On dividing equation (2) by (3), we get

$\frac{W_1}{W_2}=\frac{\frac{1}{2}{k}_1{x}_1^2}{\frac{1}{2}{k}_2{x}_2^2}$

Hence using equation (1), we get

$\frac{W_1}{W_2}=\frac{F_{x1}}{F_{x_2}}=\frac{x_1}{x_2}=\frac{k_2}{k_1}$

As $k_1>k_2$, therefore, we get,

$W_1<W_2$

Hence, more work is done on spring with spring constant $k_2$.