A particle moves under the action of a force `F=20hati + 15hatj` along a straight line `3y + alphax =5`, where, `alpha` is a constant. If the work done by the force F is zero the value of `alpha` is .

Options

A. `4/9`
B. `9/4`
C. `3`
D. `4`

Answer

D

Explanation

Let `theta_(1)` is angle on F with positive x-axis.
`:. tan theta_(1) =(F_(y))/(F_(x)) =(15)/(20) =3/4 =m_(1)` , (say) .
Slope of given line, `m_(2) = -(alpha)/(3)`
`W =0` if `FbotS`
or `m_(1)m_(2) =-1`
`:. (3/4)(-(alpha)/(3)) =-1`
`:. alpha = 4` .