A body is displaced from (0,0) to (1m, 1m) along the path x = y by a force F=x2j^+yi^N. The work done by this force will be

W=∫0,01,1F→.ds⇀ ; Here.ds⇀=dxi^+dyj^+dzk^ ∴W=∫0,01,1x2dy+ydx=∫0,01,1y2dy+xdx as x=y

A body is displaced from (0,0) to (1m, 1m) along the path x = y by a force F=x2j^+yi^N. The work done by this force will be

W=∫0,01,1F→.ds⇀ ; Here.ds⇀=dxi^+dyj^+dzk^ ∴W=∫0,01,1x2dy+ydx=∫0,01,1y2dy+xdx as x=y

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A body is displaced from (0,0) to (1m, 1m) along the path x = y by a force $F = (x^{2} \hat{j} + y \hat{i}) N$ . The work done by this force will be

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$\frac{4}{3} J$

$\frac{5}{6} J$

$\frac{3}{2} J$

$\frac{7}{5} J$

answer is B.

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$W = \int_{(0, 0)}^{(1, 1)} \vec{F} . \overset{⇀}{d s}; H e r e . \overset{⇀}{d s} = d x \hat{i} + d y \hat{j} + d z \hat{k} ∴ W = \int_{(0, 0)}^{(1, 1)} (x^{2} d y + y d x) = \int_{(0, 0)}^{(1, 1)} (y^{2} d y + x d x) (a s x = y)$

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A body is displaced from (0,0) to (1m, 1m) along the path x = y by a force F=x2j^+yi^N. The work done by this force will be

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A body is displaced from (0,0) to (1m, 1m) along the path x = y by a force $F = (x^{2} \hat{j} + y \hat{i}) N$ . The work done by this force will be