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  4. 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 :

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Q. 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 :

AIPMTAIPMT 2009Laws of Motion

Solution:

$ \vec{F}=6 \hat{i}-8 \hat{j}+10 \hat{k}$
$|\vec{F}|=\sqrt{36+64+100}$
$=\sqrt{200} N =10 \sqrt{2} N$.
Acceleration, $a=1\, ms ^{-2}$
$\therefore$ Mass, $M=\frac{10 \sqrt{2}}{1}=10 \sqrt{2} \,kg$.