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A particle in a certain conservative for...

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

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`

Text Solution

Verified by Experts

The correct Answer is:
B
Given : `V=(20xy)/z`
For a conservative field
`vecF= -vecgradV, "where" vecgrad=hati del/(delx)+hatjdel/(dely)+hatkdel/(delk)`
`therefore vecF= - [hati(delV)/(delx)+hatj(delV)/(dely)+hatk(delV)/(delz)]`
`=-[hati del/(delx)((20xy)/z)+hatjdel/(dely)((20xy)/z)+hatkdel/(delz)((20xy)/z)]`
`=-((20y)/z)hati-((20x)/z)hatj+((20xy)/z^2)hatk`
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