Given data

• Spring constant: $k = 800\,\text{N/m}$
• Initial extension: $x_1 = 5\,\text{cm} = 0.05\,\text{m}$
• Final extension: $x_2 = 15\,\text{cm} = 0.15\,\text{m}$

Work done in stretching a spring from $x_1$ to $x_2$

The elastic potential energy of a spring at extension $x$ is $U = \frac{1}{2}kx^2$

So, the work done in extending the spring from $x_1$ to $x_2$ is $W = \frac{1}{2}k\left(x_2^2 - x_1^2\right)$

Substitute the values $W = \frac{1}{2}(800)\left((0.15)^2 - (0.05)^2\right)$

First calculate the squares: $0.15^2 = 0.0225, \qquad 0.05^2 = 0.0025$

Their difference is $0.0225 - 0.0025 = 0.0200$

Therefore, $W = 400 \times 0.0200 = 8\,\text{J}$

Match with options

• A: $16\,\text{J}$
• B: $8\,\text{J}$
• C: $32\,\text{J}$
• D: $24\,\text{J}$

Hence, the correct option is B.

Comparison with stored correct answer

Stored correct answer: B

Our derived answer: B

So, the derived answer agrees with the stored correct answer.