Question

A body under the action of a force $\overrightarrow{F}=(3\hat{i}-4\hat{j}+\sqrt{11}\hat{k})\text{N}$ acquires an acceleration of $2{\text{m/s}}^2$, the mass of this body must be

• A. $4\text{kg}$
• B. $3\text{kg}$
• C. $2\text{kg}$
• D. $5\text{kg}$

Answer 1

The correct option is B $3\text{kg}$

From $2^{nd}$ law of motion, we can say that
mass of the body $m=\frac{|\overrightarrow{F}|}{a}$
Given, $\overrightarrow{F}=3\hat{i}-4\hat{j}+\sqrt{11}\hat{k}$
$\Rightarrow |\overrightarrow{F}|=\sqrt{3^2+(-4{)}^2+(\sqrt{11}{)}^2}=\sqrt{36}=6\text{N}$
$\therefore m=\frac{6}{2}=3\text{kg}$
Hence, mass of the body must be equal to $3\text{kg}$