Question

If a force \( \vec{F} = (3\hat{i} + 2\hat{j} + 5\hat{k})~\text{N} \) acting on a body displaces it through \( \vec{d} = (2\hat{i} + 2\hat{j} + 1\hat{k})~\text{m} \), then the work done by the force on the body is

• A. \( 40~\text{J} \)
• B. \( 20~\text{J} \)
• C. \( 15~\text{J} \)
• D. \( 25~\text{J} \)

Hint:

To calculate work done by a force over a displacement, take the dot product of the force and displacement vectors.

Answer 1

The Correct Option is C

Step 1: Use the formula for work done. \[ W = \vec{F} . \vec{d} \] Step 2: Compute the dot product. \[ \vec{F} . \vec{d} = (3\hat{i} + 2\hat{j} + 5\hat{k}) . (2\hat{i} + 2\hat{j} + 1\hat{k}) \] \[ = (3)(2) + (2)(2) + (5)(1) = 6 + 4 + 5 = 15~\text{J} \] % Final Answer \[ \boxed{15~\text{J}} \]