First slide

Work

Question

A particle is displaced from (1m,1m,1m) to (2m,2m,2m) under a force $\vec{F} = (2 x y \hat{i} + x^{2} \hat{j}) N$ . The work done by this force is

Moderate

A

8J
B

7J
C

16J
D

10J

Solution

$\begin{array}{l} W = \int (F_{x} d x + F_{y} d y + F_{2} d z) \\ W = \int_{(1, 1, 1)}^{(2, 2, 2)} (2 x \hat{i} + x^{2} \hat{j}) \cdot (d x \hat{i} + d y \hat{j} + d z \hat{k}) \\ W = \int_{(1, 1, 1)}^{(2, 2, 2)} 2 x y d x + x^{2} d y = \int_{(1, 1, 1)}^{(2, 2, 2)} d (x^{2} y) \\ W = {[x^{2} y]}_{(1, 1, 1)}^{(2, 2, 2)} \\ = 8 - 1 = 7 J \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App