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A horizontal force $F = (g - x^{2}) \hat{i}$ N acts on a wooden block resting on a horizontal smooth surface. The work done to move the block from $x = 0$ to $x = 3 m$ (in J) is $(g = 10 m s^{- 2})$

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Detailed Solution

$F = (g - x^{2}) \hat{i},$

work done by the force is

$d w = F d x \Rightarrow W = \int_{0}^{3} F d x = \int_{0}^{3} (g - x^{2}) d x$

$= {[g x - \frac{x^{3}}{3}]}_{0}^{3} = [3 g - \frac{3^{3}}{3}] = 21 J$

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