Q111 / 200 · NEET 2009 (Screening) · 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 $\mathrm{ms}^{-2}$. The mass of this body must be

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

Solution

Key Idea According to Newton's second law of motion, force $=$ mass $\times$ acceleration. Here, $$ \text { Here, } \begin{aligned} \quad \overrightarrow{\mathrm{F}} & =6 \hat{\mathrm{i}}-8 \hat{\mathrm{j}}+10 \hat{\mathrm{k}} \\ |\mathrm{F}| & =\sqrt{36+64+100} \\ & =10 \sqrt{2} \mathrm{~N} \\ \mathrm{a} & =1 \mathrm{~ms}^{-2} \\ \therefore \quad \mathrm{m} & =\frac{10 \sqrt{2}}{1}=10 \sqrt{2} \mathrm{~kg} \end{aligned} $$

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

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