A force `F_(1)=A hat(j)` is applied to a whose radius vector `r_(1)=ahat(i),`while a force `F_(2)=B hat(i)` is applied to the point whose radius vector `r_(2)=b hat(j).`
Both the radius vector are determined relative to the origin of the coordinate axes 0.
The moment of the force relative to 0 is

Options

A. `(aA-bB)hat(k)`
B. `(aA - bB)hatj`
C. `(ab-AB)hat(k)`
D. `(aB-bA)hat(j)`

Answer

A

Explanation

Given that
`F_(1)=A hat (j), r_(1) =a hat(i)`
`F_(2)=B hat(i),r_(2)=bhat(j)`
First case

`tau_(1)=` moment due to `F_(1)= r_(1) xx F_(1)`
`rArr tau_(1)= a hat(i)xxAhat(j)`
`tau_(1)= aAhat(k)` ...(i)
Second case

`tau_(2)=r_(2)xxF_(2)`
`tau_(2)=bhat(j)xxBhat(i)`
`tau_(2)=- bBhat(k)` ...(ii)
So, net moment is `tau = t_(1) + tau_(2)`
`rArr tau = (aA+(-bB)hat(k)`
`tau = (aA - bB)hat(k)`