Question

A particle moves from $(1,0,3)$ to the point $(-3,4,5)$, when a force $\overrightarrow{F}=(\hat{i}+5\hat{k})$ acts on it. Amount of work done in Joules is:

• A. $14$
• B. $10$
• C. $6$
• D. $15$

Answer 1

Answer: (C)

$6$

Force is given as $\overrightarrow{F}=$ $\hat{i}+5\hat{k}$
Displacement of the particle $\overrightarrow{S}=(-3\hat{i}+4\hat{j}+5\hat{k})-(\hat{i}+3\hat{k})=$ $-4\hat{i}+4\hat{j}+2\hat{k}$
Work done $W=\overrightarrow{F}.\overrightarrow{S}$
$\therefore W=$ $(\hat{i}+5\hat{k}).$ $(-4\hat{i}+4\hat{j}+2\hat{k})$
$⟹W=(-4)\left(1\right)+\left(5\right)\left(2\right)=6J$