Question

The gravitational potential due to a mass distribution is V = 3X^(2) Y+ Y^(3) Z. Find the gravitational filed.

Answer 1

answer : gravitational field is -6xy i - (3x² + 3y²z) j - y³ k

given, gravitational potential due to a mass of distribution is V = 3x²y + y²z

we know, G.F = -∆V

= -(δV/δx i + δV/δy j + δV/δz k)

so, δV/δx = δ(3x²y + y³z)/δx

= 6xy

δV/dy = δ(3x²y + y³z)/δy

= 3x² + 3y²z

δV/δz = δ(3x²y + y³z)/δz

= y³

so, G.F = -[6xy i + (3x² +3y²z) j + y³ k]

= -6xy i - (3x² + 3y²z) j - y³ k

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