First slide

Work

Question

The work done by a force $F = 2 (x + 4 y) \hat{i} + 8 x \hat{j} N$ on a particle moving from origin to (4 m, 2 m, 0) along the path x²= 8y is $10 \times n$ J. The value of n is_______

Moderate

Solution

$\begin{array}{l} W = \int \vec{F} \cdot \vec{d r} \\ = \int {2 (x + 4 y) \hat{i} + 8 x \hat{j}} \cdot (d x \hat{i} + d y \hat{j}) \\ = \int (2 x d x + 8 y d x + 8 x d y) = \int_{0}^{4} 2 x d x + 8 \int_{0, 0}^{4, 2} d (x y) \\ = [x^{2}]_{0}^{4} + 8 [x y]_{0, 0}^{4, 2} \\ = 16 + 8 \times 8 = 80 J \\ ∴ 10 n = 80 \Rightarrow n = 8 \end{array}$

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