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Question

Gravitational potential in a region is given by V=(x+y+z)J/kg.Find the gravitional intensity at (2,2,2)

A
(^i+^j+^k) N/kg
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B
2((^i+^j+^k) N/kg
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C
3((^i+^j+^k) N/kg
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D
4((^i+^j+^k) N/kg
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Solution

The correct option is A (^i+^j+^k) N/kg
V=(x+y+z)J/kg
Relation between gravitational intensity G and gravitational potential:
G=V=(x^i+y^j+z^k)([x+y+z])=^ix(x+y+z)+^jy(x+y+z)+^kz(x+y+z)=^i+^j+^k
Therefore the field is constant everywhere

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