A force acts on a particle in a plane x + y = 10. The work done by this force during a displacement from (0, 0) to (4 m , 2 m) is _____ Joule (round off to the nearest integer) [2025]

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Solution

Q.
A force $f = x^{2} y \hat{i} + y^{2} \hat{j}$ acts on a particle in a plane x + y = 10. The work done by this force during a displacement from (0, 0) to (4 m , 2 m) is _____ Joule (round off to the nearest integer) [2025]

Ans.
(152)

y = 10 – x

$W = \int_{0}^{4} x^{2} (10 - x) d x + \int_{0}^{2} y^{2} d y$

$= {[\frac{10 x^{3}}{3} - \frac{x^{4}}{4}]}_{0}^{4} + {[\frac{y^{3}}{3}]}_{0}^{2} = \frac{640}{3} - 64 + \frac{8}{3} = 152$ .

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