Laws Of Motion Ques 6
6. A body under the action of a force $\overrightarrow{\mathrm{F}}=6 \hat{\mathrm{i}}-8 \hat{\mathrm{j}}+10 \hat{\mathrm{k}}$, acquires an acceleration of $1 \mathrm{m} / \mathrm{s}^2$. The mass of this body must be
[2009]
(a) $10 $ $\mathrm{kg}$
(b) $20$ $ \mathrm{kg}$
(c) $10 \sqrt{2} $ $\mathrm{kg}$
(d) $2 \sqrt{10}$ $ \mathrm{kg}$
Show Answer
Answer:
Correct Answer: 6.(c)
Solution: (c) $ \vec{F}=6 \hat{i}-8 \hat{j}+10 \hat{k},$
$ \mid \overrightarrow{\mathrm{F}}=\sqrt{36+64+100}=10 \sqrt{2} \mathrm{N} $
$ \quad\left(\because \mathrm{F}=\sqrt{\mathrm{F}_{\mathrm{x}}^2+\mathrm{F} _{\mathrm{y}}^2+\mathrm{F} _{\mathrm{z}}^2}\right)$
Given, $a=1 \mathrm{ms}^{-2}$
$\because \mathrm{F}=\mathrm{ma} \Rightarrow \mathrm{m}=\frac{10 \sqrt{2}}{1}=10 \sqrt{2} $ $\mathrm{kg}$
BETA
