First slide

Work

Question

The work done by a force of $(\hat{i} +2 \hat{j})$ is zero, when a particle is moving along the line $4 y + k x = 3$ . The value of K is ________

Difficult

Solution

$\begin{array}{l} W = \vec{F} \cdot \vec{Δr} = (\hat{i} + 2 \hat{j}) \cdot (Δx \hat{i} + Δy \hat{j}) \\ 0 = Δ x + 2 Δ y \\ \frac{Δ y}{Δ x} = - \frac{1}{2} \\ 4 y + k x = 3 \\ y = \frac{- kx}{4} + \frac{3}{4} \\ \frac{Δ y}{Δ x} = \frac{- k}{4} \Rightarrow= \frac{- 1}{2} = \frac{- k}{4} \\ k = 2 \end{array}$

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