Question

A force $\overrightarrow{F}=(5\hat{i}+4\hat{j})N$ displaces the body by $\overrightarrow{s}=(3\hat{i}+5\hat{k})m$ in $3s.$ Power generated will be

• A. $11W$
• B. $6W$
• C. $5W$
• D. $12W$

Answer 1

The correct option is C $5W$

$\begin{array}{c}F=\left(5\hat{i}+4\hat{j}\right)=\left(5\hat{i}+4\hat{j}+0\hat{k}\right)\\ s=\left(3\hat{i}+4\hat{j}\right)=\left(3\hat{i}+0\hat{j}+4\hat{k}\right)\end{array}$

Work done $\left(w\right)=f.s$

$\begin{array}{c}=\left(5\hat{i}+4\hat{j}+0\hat{k}\right).\left(3\hat{i}+0\hat{j}+4\hat{k}\right)\\ =\left(5\times 3\right)+\left(4\times 0\right)+\left(0\times 4\right)\\ =15J\end{array}$

So, $w=15J$

Power $\left(p\right)=\frac{w}{t}=\frac{15J}{3\sec }$

$\begin{array}{c}=5J/s\\ =5watt\end{array}$

$\therefore$ The power is $5$ watt.