Question:
A particle moves from position \(3\hat{i}+2\hat{j}-6\hat{k}\) to \(14\hat{i}+13\hat{j}+9\hat{k}\) due to uniform force of \((4\hat{i}+\hat{j}+3\hat{k})\) N. If displacement is in metre then work done will be
A particle moves from position \(3\hat{i}+2\hat{j}-6\hat{k}\) to \(14\hat{i}+13\hat{j}+9\hat{k}\) due to uniform force of \((4\hat{i}+\hat{j}+3\hat{k})\) N. If displacement is in metre then work done will be
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Work done by a uniform force equals the dot product of force and displacement vectors.
Updated On: Nov 12, 2026
- \(100\) J
- \(200\) J
- \(300\) J
- \(250\) J
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept
For a constant force, work done is \(W=\vec{F}\cdot\vec{d}\), where \(\vec{d}\) is the displacement.
Step 2: Find the Displacement
\(\vec{d}=(14-3)\hat{i}+(13-2)\hat{j}+(9+6)\hat{k}=11\hat{i}+11\hat{j}+15\hat{k}\) m
Step 3: Calculation
\(W=(4)(11)+(1)(11)+(3)(15)=44+11+45=100\) J
Step 4: Compare the options
The work done is \(100\) J, which is option (A).
Final Answer:
The work done is 100 joules. \[ \boxed{\text{(A) }100\ \text{J}} \]
For a constant force, work done is \(W=\vec{F}\cdot\vec{d}\), where \(\vec{d}\) is the displacement.
Step 2: Find the Displacement
\(\vec{d}=(14-3)\hat{i}+(13-2)\hat{j}+(9+6)\hat{k}=11\hat{i}+11\hat{j}+15\hat{k}\) m
Step 3: Calculation
\(W=(4)(11)+(1)(11)+(3)(15)=44+11+45=100\) J
Step 4: Compare the options
The work done is \(100\) J, which is option (A).
Final Answer:
The work done is 100 joules. \[ \boxed{\text{(A) }100\ \text{J}} \]
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