Question

# A $40mm$ long spring is stretched by applying a force. If $10N$ force is required to stretch the spring through one mm, then work done in stretching the spring through $40mm$ is:

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Solution

## Step 1: Given dataLength of the spring (L) = $40mm$Force (F) applied to stretch the spring by one mm ($0.001m$) = $10N$Step 2: Formula used$F=kx$, where F is the force applied to stretch the spring, k is the spring constant and x is the displacement.$W=\frac{1}{2}k{x}^{2}$, where W is the work done to deform the spring.Step 3: Find the spring constantHooke's law states that:$F=kx$On substituting the given values in the formula, we get:$10=k×{10}^{-3}\phantom{\rule{0ex}{0ex}}⇒k={10}^{4}N/m$Step 4: Calculate work doneThe formula for work done in stretching a spring is:$W=\frac{1}{2}k{x}^{2}$It is given that $x=40mm=0.04m$.On substituting the given values in the formula, we get:$W=\frac{1}{2}×{10}^{4}×{\left(0.04\right)}^{2}\phantom{\rule{0ex}{0ex}}W=8J$Thus, the work done in stretching the spring through $40mm$ is $8J$.

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