Two forces F̅1 = î - ĵ + k̂ and F̅2 = 4î + 2ĵ + 3k̂ act on a particle and displace it from the point (0, 1, 2) to (1, -2, 3), then the total work

1 Answer

answered Mar 1, 2022 by VinayPoonia (113k points)
selected Mar 1, 2022 by Rohitpatil

Best answer

Correct Answer - Option 2 : 6 unit

Concept Used:

Net Force 'F' = F̅1 + F̅₂

The displacement vector 'd' = (Final position − Initial position)

Work done = F.d

Calculation:

Net Force 'F' = F̅1 + F̅₂

F = î - ĵ + k̂ + F̅2 = 4î + 2ĵ + 3k̂ = î - 3ĵ + 4k̂

Now, Let the Point (0, 1, 2) to (1, -2, 3) be 0î + ĵ + 2k̂ and î - 2ĵ + 3k̂ respectively

The displacement vector 'd' = î - 2ĵ + 3k̂ - (0î + ĵ + 2k̂) = î - 3 ĵ + k̂

Work done = F.d

⇒ (î - 3ĵ + 4k̂) . (î - 3 ĵ + k̂) = 5 - 3 + 4 = 6 unit

∴ The total work done = 6 unit

\(\widehat j . \widehat j = 1\)

\(\widehat i . \widehat i = 1\)

\(\widehat k . \widehat k = 1\)

Other combinations of dot products are equal to zero

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