Question

A spring of spring constant $5x{10}^{3}N{m}^{-1}$ is stretched initially by $5cm$ from the unstretched position. Then the work required to stretch it further by another $5cm$is

• A. $12.50N–m$
• B. $18.75N–m$
• C. $25N–m$
• D. $6.25N–m$

Answer 1

The correct option is B

$18.75N–m$

Step 1: Given data

Spring constant $k=5x{10}^{3}N{m}^{-1}$

Stretched position $x_1=5cm$

Step 2: Find the work required to stretch it further

The work done is given by,

$$\begin{gathered} W_1=(1/2)k{x}_1^2 \\ {W}_1=(1/2)(5\times {10}^3){(5\times {10}^{-2})}^2 \\ {W}_1=6.25J \end{gathered}$$

After additional compression, the work done is

$$\begin{gathered} W_2=(1/2)k{x}_2^2 \\ {W}_2=(1/2)(5\times {10}^3){(10\times {10}^{-2})}^2 \\ {W}_2=25J \end{gathered}$$

The additional work done is

$$\begin{gathered} =W_2–W_2 \\ =25-6.25 \\ =18.75J \\ =18.75N-m \end{gathered}$$

Hence, option B is correct.