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Laws of Motion question

2024 · 1 Feb · Shift 2 · Q62

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Laws of Motion
2024 · 1 Feb · Shift 2 · Q62

Laws of Motion question

2024 · 1 Feb · Shift 2 · Q62

JEE MainPhysicsLaws of MotionMCQ+4 / −1

A body of mass

4 \mathrm{~kg}

experiences two forces

\vec{F}_1=5 \hat{i}+8 \hat{j}+7 \hat{k}

and

\overrightarrow{\mathrm{F}}_2=3 \hat{i}-4 \hat{j}-3 \hat{k}

. The acceleration acting on the body is :

A
$2 \hat{i}+\hat{j}+\hat{k}$
B
$4 \hat{i}+2 \hat{j}+2 \hat{k}$
C
$-2 \hat{i}-\hat{j}-\hat{k}$
D
$2 \hat{i}+3 \hat{j}+3 \hat{k}$

View written solutionFree

Correct answer: A

Given data

Mass of the body: $m=4\,\text{kg}$
Forces: $\vec F_1=5\hat i+8\hat j+7\hat k$ $\vec F_2=3\hat i-4\hat j-3\hat k$

Find the net force

The resultant force is: $\vec F=\vec F_1+\vec F_2$

So, $\vec F=(5+3)\hat i+(8-4)\hat j+(7-3)\hat k$ $\vec F=8\hat i+4\hat j+4\hat k$

Use Newton's second law

$\vec F=m\vec a$

Therefore, $\vec a=\frac{\vec F}{m}$

$\vec a=\frac{8\hat i+4\hat j+4\hat k}{4}$

$\vec a=2\hat i+\hat j+\hat k$

Match with the options

A: $2\hat i+\hat j+\hat k$ ✓
B: $4\hat i+2\hat j+2\hat k$ ✗
C: $-2\hat i-\hat j-\hat k$ ✗
D: $2\hat i+3\hat j+3\hat k$ ✗

Hence, the correct answer is Option A.

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