Question:
A body of mass 2 kg is moving with a constant acceleration of $(2\hat{i} + 3\hat{j} - \hat{k})ms^{-2}$ If the displacement made by the body is $(3\hat{i} - \hat{j} + 2\hat{k})$ m then the work done is
A body of mass 2 kg is moving with a constant acceleration of $(2\hat{i} + 3\hat{j} - \hat{k})ms^{-2}$ If the displacement made by the body is $(3\hat{i} - \hat{j} + 2\hat{k})$ m then the work done is
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Work = $m(\vec{a} \cdot \vec{S})$. Calculate the dot product of acceleration and displacement first, then multiply by mass.
Updated On: Jul 4, 2026
- 2 J
- 10 J
- 12 J
- 22 J
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The Correct Option is A
Solution and Explanation
Step 1: Concept
Work done $W$ is the dot product of Force and Displacement ($\vec{F} \cdot \vec{S}$). Force is $\vec{F} = m\vec{a}$.
Step 2: Meaning
$\vec{F} = 2 \text{ kg} \times (2\hat{i} + 3\hat{j} - \hat{k}) = (4\hat{i} + 6\hat{j} - 2\hat{k})$ N.
Step 3: Analysis
$W = (4\hat{i} + 6\hat{j} - 2\hat{k}) \cdot (3\hat{i} - \hat{j} + 2\hat{k})$. Calculate the dot product: $(4 \times 3) + (6 \times -1) + (-2 \times 2)$.
Step 4: Conclusion
$W = 12 - 6 - 4 = 2$ J. Final Answer: (A)
Work done $W$ is the dot product of Force and Displacement ($\vec{F} \cdot \vec{S}$). Force is $\vec{F} = m\vec{a}$.
Step 2: Meaning
$\vec{F} = 2 \text{ kg} \times (2\hat{i} + 3\hat{j} - \hat{k}) = (4\hat{i} + 6\hat{j} - 2\hat{k})$ N.
Step 3: Analysis
$W = (4\hat{i} + 6\hat{j} - 2\hat{k}) \cdot (3\hat{i} - \hat{j} + 2\hat{k})$. Calculate the dot product: $(4 \times 3) + (6 \times -1) + (-2 \times 2)$.
Step 4: Conclusion
$W = 12 - 6 - 4 = 2$ J. Final Answer: (A)
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