First slide

Work

Question

The work done by a force of $(2 x \hat{i} + 30 \hat{j}) N$ in displacing the particle from (1,0,2) m to (2,y,2) m is zero. The value of y is

Moderate

A

1
B

-1
C

3
D

-3

Solution

$\begin{array}{l} W = \int F_{x} d x + \int F_{y} d y \\ 0 = \int_{1}^{2} 2 x d x + \int_{0}^{y} 3 d y \\ 0 = 2 {[\frac{x^{2}}{2}]}_{1}^{2} + 3 (y - 0) \\ 0 = 3 + 3 y \Rightarrow y = - 1 \end{array}$

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