Q98 / 197 · NEET 2009 (Mains) · Physics

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 :

  • Correct answer
    A
    $10 \sqrt{2} \mathrm{~kg}$
  • B
    $2 \sqrt{10} \mathrm{~kg}$
  • C
    $10 \mathrm{~kg}$
  • D
    $20 \mathrm{~kg}$

Solution

$$ \begin{aligned} \overrightarrow{\mathrm{F}} & =6 \hat{\mathrm{i}}-8 \hat{\mathrm{j}}+10 \hat{\mathrm{k}} \\ |\overrightarrow{\mathrm{F}}| & =\sqrt{6^2+8^2+10^2}=10 \sqrt{2} \\ \mathrm{~m} & =\frac{|\overrightarrow{\mathrm{F}}|}{\mathrm{a}}=\frac{10 \sqrt{2}}{1}=10 \sqrt{2} \mathrm{~kg} \end{aligned} $$

Hence, the correct answer is option: 'A'.

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