Question

A uniform force of $(3 \hat{i} + \hat{j})$ newton acts on a particle of mass 2kg. 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 :

• A. 15 J
• B. 9 J
• C. 6 J
• D. 13 J

Answer 1

The Correct Option is B

The correct answer is B:9J
\(W = \vec{F}. \vec{S} = (3\hat{i} + \hat{j}) .[(4 -2) \hat{i} + (3 - 0) \hat{j} + ( - 1 - 1)\hat{k}]\)
\(= (3\hat{i} + \hat{j}) .(2\hat{i} + 3 \hat{j} - 2\hat{k})\)
\(= 3(2) + 1(3) + 0( - 2) = 9 \,\,J\)