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(B) The work done $W$ in stretching a spring by an extension $x$ is given by $W = \frac{1}{2} k x^2$. The work done in stretching the spring from an i

Vedclass · Accepted Answer

Less than the work done in stretching it from $20 \ cm$ to $30 \ cm$.

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(B) The work done $W$ in stretching a spring by an extension $x$ is given by $W = \frac{1}{2} k x^2$. The work done in stretching the spring from an initial extension $x_1$ to a final extension $x_2$ is given by $W = \frac{1}{2} k (x_2^2 - x_1^2)$. For the first case ($10 \ cm$ to $20 \ cm$): $W_1 = \frac{1}{2} k (20^2 - 10^2) = \frac{1}{2} k (400 - 100) = 150 k$. For the second case ($20 \ cm$ to $30 \ cm$): $W_2 = \frac{1}{2} k (30^2 - 20^2) = \frac{1}{2} k (900 - 400) = 250 k$. Comparing the two,$W_1 < W_2$. Therefore,the work done in stretching the spring from $10 \ cm$ to $20 \ cm$ is less than the work done in stretching it from $20 \ cm$ to $30 \ cm$.

The work done in stretching a spring from $10 \ cm$ to $20 \ cm$ is:

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