A body of mass 4 kg experiences two forces $\overrightarrow{\mathrm{F}}_{1}=5 \hat{\mathrm{i}}+8 \hat{\mathrm{j}}+7 \hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{F}}_{2}=3 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}$. The acceleration acting on the body is :

(C) $2 \hat{i}+\hat{j}+\hat{k}$

(A) $-2 \hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}}$

(B) $4 \hat{i}+2 \hat{j}+2 \hat{k}$

(D) $2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}$

JEE Main · 2024 · 01 Feb 2024 · Shift 2 · Laws of Motion

A body of mass 4 kg experiences two forces

F_{1} = 5 \hat{i} + 8 \hat{j} + 7 \hat{k}

and

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) $2 \hat{i} + \hat{j} + \hat{k}$ ✓ Correct
(D) $2 \hat{i} + 3 \hat{j} + 3 \hat{k}$

Answer: (C)

Solution

The net force is

F = F_{1} + F_{2} = (5 + 3) \hat{i} + (8 - 4) \hat{j} + (7 - 3) \hat{k} = 8 \hat{i} + 4 \hat{j} + 4 \hat{k}

. By Newton's second law,

a = \frac{F}{m} = \frac{8 i ^ + 4 j ^ + 4 k ^}{4} = 2 \hat{i} + \hat{j} + \hat{k}

JEE Main · 2024 · 01 Feb 2024 · Shift 2 · Single correct option

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