First slide

Work done by Diff type of forces

Question

A uniform force of $(3 \hat{i} + \hat{j})$ newton acts on a particle of mass 2 kg. Hence the particle is displaced from position $(2 \hat{i} + \hat{k})$ meter to position $(4 \hat{i} + 3 \hat{j} - \hat{k})$ meter. The work done by the force on the particle is

Easy

A

15 J
B

9 J
C

6J
D

13J

Solution

$\begin{array}{l} W = \vec{F} \cdot \vec{S} = (3 \hat{i} + \hat{j}) \cdot [(4 - 2) \hat{i} + (3 - 0) \hat{j} + (- 1 - 1) \hat{k}] \\ = (3 \hat{i} + \hat{j}) \cdot (2 \hat{i} + 3 \hat{j} - 2 \hat{k}) = 3 (2) + 1 (3) + 0 (- 2) = 9 J \end{array}$

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