A spring requires 12 J of work to compress it by 4 cm. How much work is required to stretch it by 3 cm from its unstretched length?

The work $W$ done to compress or stretch a spring by a displacement $x$ from its unstretched length is given by:

where $k$ is the spring constant.

Initial compression $x_1 = 4 \text{ cm} = 0.04 \text{ m}$.
New stretch $x_2 = 3 \text{ cm} = 0.03 \text{ m}$.

Given $W_1 = 12 \text{ J}$ for $x_1 = 0.04 \text{ m}$.

We need to find $W_2$ for $x_2 = 0.03 \text{ m}$.

The correct option is B) 6.75 J.