Question

A uniform force of \((4i + 3j) N acts on a body. The body is displaced from (4i - 3j - 2k)\,m to (5i - 4j + 2k)\,m. Then the work done by the force on the body is in joule:

• A. 1
• B. 5
• C. 7
• D. 11

Hint:

Work done by a force depends only on the dot product of force and displacement vectors, not on the path taken.

Answer 1

The Correct Option is A

Step 1: Force vector.
F = 4i + 3j.

Step 2: Displacement vector.
Initial position: 4i - 3j - 2k; final position: 5i - 4j + 2k; displacement d = (5-4)i + (-4+3)j + (2+2)k = i - j + 4k.

Step 3: Work calculation.
W = F·d = (4)(1) + (3)(-1) + (0)(4) = 4 - 3 = 1 J.

Step 4: Conclusion.
The work done is 1 J.