Question

A body of mass 2 kg is at rest. A force of $4\hat{i}+3\hat{j}-5\hat{k}$ N acts on it and displaces through $2\hat{i}+\hat{j}+2\hat{k}$ m. The velocity acquired by the body is:

• A. $0m{s}^{-1}$
• B. $1m{s}^{-1}$
• C. $2m{s}^{-1}$
• D. $10m{s}^{-1}$

Answer 1

The correct option is B $1m{s}^{-1}$

$W.D=\Delta (K.E)=\frac{1}{2}m{v}^2=\overrightarrow{F}.\overrightarrow{s}$

$=(4\hat{i}+3\hat{j}-5\hat{k}).(2\hat{i}+1\hat{j}+2\hat{k})$

$=8+3-10$

$=1$

$\Rightarrow \frac{1}{2}m{v}^2=1$

$\Rightarrow \frac{1}{2}\times 2v^2=1$

$\Rightarrow v=1m/s$