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A force vecF=6xhati+2yhatj displaces a b...

A force `vecF=6xhati+2yhatj` displaces a body from `vecr_1=3hati+8hatj` to `vecr_2=5hati-4hatj`. Find the work done by the force.

A

`91 J`

B

`0 J`

C

`182 J`

D

`45.5 J`

Text Solution

Verified by Experts

The correct Answer is:
B
Given force `vecF=6xhati+2yhatj`
Initial position `vecr_1=3hati+8hatj` and final position `vecr_2=5hati-4hatj`
We know work done, `W=underset(s_1)overset(s_2)intvecF.dvecs=underset(s_1)overset(s_2)vecF*(dxhati+dyhatj)`
`W=underset(s_1)overset(s_2)int(6xhati+2yhatj)*(dxhati+dyhatj)`
`=underset3overset5int6xdx+underset8overset(-4)int2ydy`
`=[3x^2]_3^5+[y^2]_8^-4=[75-27]+[16-64]=0J`
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