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

W = ∫ 0,0 1,1 F → . d → x Here, d → s = d x i ^ + d y j ^ + d z k ^ ∴ W = ∫ 0,0 1,1 x 2 d y + y d x = ∫ 0,0 1,1 x 2 d y + x . d x (As, x = y ) ∴ W = y 3 3 + x 2 2 0,0 1,1 = 5 6 J

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PhysicsW.E.P.MiscellaneousEasy2 minPYQ_2020

PhysicsEasysingle choice

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

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Answer:

Solution:

$W = \int_{(0,0)}^{(1,1)} \vec{F} . \vec{d} x$

Here, $\vec{d} s = d x \hat{i} + d y \hat{j} + d z \hat{k}$

$∴ W = \int_{(0,0)}^{(1,1)} (x^{2} d y + y d x)$

$= \int_{(0,0)}^{(1,1)} (x^{2} d y + x . d x)$

(As, $x = y$ )

$∴ W = {[\frac{y^{3}}{3} + \frac{x^{2}}{2}]}_{(0,0)}^{(1,1)} = \frac{5}{6} J$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:W.E.P.Subtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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