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Work done by a force F on a body is W ...

Work done by a force F on a body is W = F .s, where s is the displacement of body. Given that under a force `F = (2 hat I +3 hat j +4 hat k) N` a body is displaced from position vector `r_1 = (2 hat I +3 hat j + hat k) m` to the position vector `r_2 = (hat i +hat j+ hat k) m`. Find the work done by this force.

A

`4J`

B

`10J`

C

`-16J`

D

`-8J`

Text Solution

Verified by Experts

The correct Answer is:
D
The body is displaced from `r_1 or r_2`. Therefore, displacement of the body is `s = r_2 - r_1 = (hat I +hat j + hat k)-(2hati+3hatj+ hat k) = (-hati- 2 hat j)m`
Now, work done by the force is `W = F.s `
`=(2hati+3hatj+4hatk).(-hat I - 2 hatj)`
`=(2)(-1) + (3)(-2) + (4)(0) = -8 J`
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