Question

# Gravitational field in x−y plane is given as →g=(2x^i+3y2^j) N/kg. The difference in gravitational potential between 2 points A(2,4) & B(6,0) is

A
VAVB=32 J/kg
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B
VAVB=64 J/kg
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C
VAVB=64 J/kg
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D
VAVB=32 J/kg
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Solution

## The correct option is D VA−VB=−32 J/kgGiven gravitational field is →g=(2x^i+3y2^j) N/kg Relation between gravitational field and gravitational potential is −dV=→g⋅→dr ⇒−dV=(2x^i+3y2^j).(dx^i+dy^j) −dV=2xdx+3y2dy Integrate both sides from point A(2,4) to point B(6,0) ∴B∫A−dV=26∫2xdx+30∫4y2dy ⇒VA−VB=2[x22]62+3[y33]04 ⇒VA−VB=22[36−4]+33[0−64] ∴VA−VB=−32 J/kg Hence, option (d) is the correct choice.

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