Question:
Due to a force of \((6\hat{i} + 2\hat{j})\ \text{N\) the displacement of a body is \((3\hat{i} - \hat{j})\ \text{m}\), then the work done is}
Due to a force of \((6\hat{i} + 2\hat{j})\ \text{N\) the displacement of a body is \((3\hat{i} - \hat{j})\ \text{m}\), then the work done is}
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Work is a scalar product (dot product). Only the component of force along displacement does work.
Updated On: Apr 23, 2026
- \(16\ \text{J}\)
- \(12\ \text{J}\)
- \(8\ \text{J}\)
- zero
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
Work done \(W = \vec{F} \cdot \vec{d} = F_x d_x + F_y d_y\).
Step 2: Detailed Explanation:
\(\vec{F} = 6\hat{i} + 2\hat{j}\), \(\vec{d} = 3\hat{i} - \hat{j}\).
\(W = (6)(3) + (2)(-1) = 18 - 2 = 16\ \text{J}\).
Step 3: Final Answer:
Thus, work done = \(16\ \text{J}\).
Work done \(W = \vec{F} \cdot \vec{d} = F_x d_x + F_y d_y\).
Step 2: Detailed Explanation:
\(\vec{F} = 6\hat{i} + 2\hat{j}\), \(\vec{d} = 3\hat{i} - \hat{j}\).
\(W = (6)(3) + (2)(-1) = 18 - 2 = 16\ \text{J}\).
Step 3: Final Answer:
Thus, work done = \(16\ \text{J}\).
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