Q139 / 180 · COMEDK 2020 · Physics

A body under the action of a force $\mathbf{F}=6 \hat{\mathbf{i}}-8 \hat{\mathbf{j}}+10 \hat{\mathbf{k}}$, acquires an acceleration of $1 \mathrm{~m} / \mathrm{s}^{2}$. The mass of this body must be

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

Solution

Given, $\mathbf{F}=6 \hat{\mathbf{i}}-8 \hat{\mathbf{j}}+10 \hat{\mathbf{k}}$ $$ \begin{aligned} a &=1 \mathrm{~m} / \mathrm{s}^{2} \\ |\mathbf{F}| &=\sqrt{6^{2}+(-8)^{2}+10^{2}} \\ &=\sqrt{200} \\ \Rightarrow \quad|\mathbf{F}| &=10 \sqrt{2} \mathrm{~N} \\ \Rightarrow \quad m a &=10 \sqrt{2} \\ \Rightarrow \quad m &=\frac{10 \sqrt{2}}{a} \\ &=\frac{10 \sqrt{2}}{1} \\ &=10 \sqrt{2} \mathrm{~kg} \end{aligned} $$

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

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