Question

Two springs of force constant $100N/m$ and $150N/m$ are in series as shown. The block is pulled by a distance of $2.5cm$ to the right from equilibrium position. What is the ratio of work done by the spring at left to the work done by the spring at right?

• A. $\frac{3}{2}$
• B. $\frac{2}{3}$
• C. $0.2$
• D. $0.5$

Answer 1

The correct option is A

$\frac{3}{2}$

Assume that the extension in left spring is $x_1$ and in right spring is $x_2$. So,
$k_1=100N/m$
$k_2=150N/m$

When connected in series, the force in both the springs is the same. Hence,
$k_1{x}_1=k_2{x}_2$
$100x_1=150x_2$
$x_1=1.5x_2$

The work done in the spring is stored as potential energy, hence
$W=\frac{1}{2}k{x}^2$

$\therefore \frac{W_1}{W_2}=\frac{\frac{1}{2}{k}_1{x}_1^2}{\frac{1}{2}{k}_2{x}_2^2}=\frac{x_1}{x_2}=\frac{3}{2}$