A body, under the action of a force F =6 i -8 j +10 k , acquires an acceleration of 1 ms^ -2 . The mass of this body must be

Correct answer: D. 10 2 ~kg Key Idea According to Newton's second law of motion, force = mass × acceleration. Here, Here, aligned F & =6 i -8 j +10 k |F|& = 36+64+100 & =10 2 ~N a& =1 ~ms^ -2 m& = 10 2 1 =10 2 ~kg aligned

NEET 2009

Exam: NEET
Year: 2009
Subject: Physics
Chapter: Laws of Motion

NEET 2009 · Physics · Laws of Motion

A body, under the action of a force F =6 i -8 j +10 k , acquires an...

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

Options

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

Correct answer

D. $10 \sqrt{2} \mathrm{~kg}$

Step-by-step 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}

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