A particle acted by constant forces `4 hat i+ hat j-3 hat ka n d3 hat i+ hat9- hat k` is displaced from point ` hat i+2 hat j+3 hat k` to point `5 hat i+4 hat j+ hat kdot` find the total work done by the forces in units.

Options

A. 20J
B. 24J
C. 50J
D. 30J

Answer

B

Explanation

Net force `vec(F) = 4hat(i) + hat(j) - 3hat(k) + 3hat(i) + hat(j) - hat(k)`
`= (7hat(i) + 2hat(j) - 4hat(k))N`
displacement `vec(S)` = final position - initial position
`=(5 hat(i) + 4hat(j)- hat(k)) - (hat(i) + 2hat(j)- 3 hat(k))`
`=4 hat(i) + 2hat(j) + 2hat(k)`
Work done `W= vec(F).vec(S)`
`= 28+ 4- 8= 24J`