Question

A spring stores $1J$ of energy for compression of $1mm$. The additional work to be done to compress it further by $1mm$ is

• A. $1J$
• B. $2J$
• C. $3J$
• D. $4J$
• E. $0.5J$

Answer 1

The correct option is C

$3J$

Step 1: Given data

Energy, $W_1=1J$

Compression $x_1=1mm$

Compression $x_2=2mm$

Step 2: Find the additional work done

The work done is given by,

$$\begin{gathered} W_1=(1/2)k{x}_1^2 \\ 1=(1/2)k{(1\times {10}^{-3})}^2 \\ k=2\times {10}^6 \end{gathered}$$

After additional compression, the work done is

$$\begin{gathered} W_2=(1/2)k{x}_2^2 \\ {W}_2=(1/2)(2\times {10}^6){(2\times {10}^{-3})}^2 \\ {W}_2=4J \end{gathered}$$

The additional work done is

$$\begin{gathered} =W_2–W_2 \\ =4-1 \\ =3J \end{gathered}$$

Hence, option C is correct.