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A particle in a certain conservative force field has a potential energy given by `V=(20xy)/z`. The force exerted on it isA. `((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` |
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Answer» Correct Answer - 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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