Question

A body of mass 10 kg id displaced from point A(2, 1, 3) to point B(3, 3, 4) under the effect of a force of magnitude 20 N in the direction of $6\overrightarrow{i}+8\overrightarrow{j}$. Calculate W.D. by the force :-

• A. $22J$
• B. $20\sqrt{6}J$
• C. $44J$
• D. Zero

Answer 1

Answer: (C)

$44J$

$\overrightarrow{d}=\overrightarrow{B}-\overrightarrow{A}=(4-3)\hat{k}+(3-1)\hat{j}+(3-2)\hat{i}$
$\overrightarrow{d}=\hat{i}+2\hat{j}+\hat{k}$

$\overrightarrow{F}=|F|\hat{F}$

$\overrightarrow{r}=6\hat{i}+8\hat{j}$

$\overrightarrow{F}=20\left[\frac{6\hat{i}+8\hat{j}}{10}\right]$

$=2[6\hat{i}+8\hat{j}]$

$W=\overrightarrow{F}.\overrightarrow{d}=(\hat{i}+2\hat{j}+\hat{k})\cdot 2[6\hat{i}+8\hat{j}]$

$\overrightarrow{F}.\overrightarrow{d}=2[6+16]=44J$