Question

A force \( (5i - 2j + 3k) \, \text{N} \) acts on a body of mass 2 kg and displaces it from \( (3i + 2j - k) \, \text{m} \) to \( (6i - j + 4k) \, \text{m} \). The work done is

• A. 27 J
• B. 18 J
• C. 36 J
• D. 9 J

Hint:

Work is calculated as the dot product of the force and displacement vectors. Be sure to subtract the initial and final position vectors before applying the dot product.

Answer 1

The Correct Option is C

Step 1: Understanding the work formula.
Work done \( W \) is given by the dot product of the force and displacement vectors: \[ W = \vec{F} \cdot \vec{d} \] where \( \vec{F} = (5i - 2j + 3k) \, \text{N} \) and the displacement \( \vec{d} = (6i - j + 4k) - (3i + 2j - k) = (3i - 3j + 5k) \, \text{m} \).
Step 2: Computing the dot product.
Now, the work done is: \[ W = (5i - 2j + 3k) \cdot (3i - 3j + 5k) \] Performing the dot product: \[ W = 5 \times 3 + (-2) \times (-3) + 3 \times 5 = 15 + 6 + 15 = 36 \, \text{J} \] Step 3: Conclusion.
The correct answer is (C), 36 J.