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A variable force $\vec{F} = (x^{2} \hat{i} + xy \hat{j}) N$ is acting on a particle which moves from point (0, 0) to (1 m , 2 m) along the path OAB as shown. The work done by force is $\frac{p}{q}$ joules, where p and q are co-prime integers. Find the value of $(p + q)$ .

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answer is 10.

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Detailed Solution

$W = W_{OA} + W_{AB} = \int_{0}^{1} x^{2} dx + \int_{0}^{2} y dy = \frac{1}{3} + \frac{4}{2} = \frac{7}{3} J \Rightarrow p + q = 10$

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