Laws of Motion - Result Question 5

5. A body under the action of a force

$\vec{F}=6 \hat{i}-8 \hat{j}+10 \hat{k}$, acquires an acceleration of $1 m / s^{2}$. The mass of this body must be [2009]

(a) $10 kg$

(b) $20 kg$

(c) $10 \sqrt{2} kg$

(d) $2 \sqrt{10} kg$

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Answer:

Correct Answer: 5. (c)

Solution:

  1. (c) $\vec{F}=6 \hat{i}-8 \hat{j}+10 \hat{k}$,

$|\overrightarrow{{}F}|=\sqrt{36+64+100}=10 \sqrt{2} N$

$(\because F=\sqrt{F_x^{2}+F_y^{2}+F_z^{2}})$

Given, $a=1 ms^{-2}$

$\because F=ma \Rightarrow m=\frac{10 \sqrt{2}}{1}=10 \sqrt{2} kg$