Question

If a constant force of \((2i + 3j + 4k) \, \text{N}\) acting on a body of mass \(5 \, \text{kg}\) displaces it from \((3i - 4k)\, \text{m}\) to \((2i + 2j + 3k)\, \text{m}\), then the work done by the force on the body is:

• A. 32 J
• B. 28 J
• C. 36 J
• D. 44 J

Hint:

Use the dot product to calculate work done when the force and displacement vectors are given in component form.

Answer 1

The Correct Option is A

The work done by a force is given by the dot product of force and displacement: \[ W = \vec{F} . \vec{d}. \] First, find the displacement vector: \[ \vec{d} = (2i + 2j + 3k) - (3i - 4k) = -i + 2j + 7k. \] Now calculate the dot product: \[ W = (2i + 3j + 4k) . (-i + 2j + 7k) = (2 \times -1) + (3 \times 2) + (4 \times 7) = -2 + 6 + 28 = 32 \, \text{J}. \]