Question

A particle is displaced from position r1 = (3i + 2j - 6k) to another position r2 = (14i + 13j + 9k) under the impact of a force of 5i newton. The work done will be given by?

1) 15 joules
2) 30 joules
3) 45 joules
4) 60 joules

Answer 1

The work done when a particle is displaced from one position to another under a constant force is the dot product of the force and displacement vectors. Given vectors, the work can be calculated and in this scenario, it equals 55 joules, which does not match any of the answer choices provided.

Step-by-step explanation:

The work done on a particle when it is displaced under the force is given by the dot product of the force vector and the displacement vector. In this case, the displacement (Δr) is r2 - r1, which is (14i + 13j + 9k) - (3i + 2j - 6k) = 11i + 11j + 15k. The work done (W) is then the dot product of the force (5i newton) and the displacement (Δr). Hence, W = 5i ⋅ (11i + 11j + 15k) = 5 × 11 + 5 × 0 + 5 × 0 = 55 joules, which is not one of the options provided. Therefore, the answer is that none of the options are correct.