Two particles of masses m and 4m are fixed at x=0 and x=5a. At the point between them where the net gravitational field is zero, the gravitational potential is:
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Two particles of masses m and 4m are fixed at x=0 and x=5a. At the point between them where the net gravitational field is zero, the gravitational potential is:

G1 Physics · Accepted Answer

Let the point be at distance x from m. Gm/x²=4Gm/(5a−x)² ⇒ 5a−x=2x ⇒ x=5a/3. Therefore V=−Gm/(5a/3)−4Gm/(10a/3)=−3Gm/(5a)−6Gm/(5a)=−9Gm/(5a).