A particle in a certain conservative force field has a potential energy given by `V=(20xy)/z`. The force exerted on it is

Options

A. `((20y)/(z))hati+((20x)/(z))hatj+((20xy)/(z^2))hatk`
B. `-((20y)/(z))hati-((20x)/(z))hatj+((20xy)/(z^2))hatk`
C. `-((20y)/(z))hati-((20x)/(z))hatj-((20xy)/(z^2))hatk`
D. `((20y)/(z))hati+((20x)/(z))hatj-((20xy)/(z^2))hatk`

Answer

B

Explanation

`U = (20 xy)/(z)`
`F = -[(delU)/(delx)hati+(delU)/(dely)hatj+(delU)/(delz)hatk]`
`=(-20y)/zhati-(20x)/z hatj+(20 xy)/z^2 hatk`