Two particles of masses m and 4m are fixed at x=0 and x=5a. A test particle is placed between them where net gravitational field is zero. The gravitational potential there is:
Options

Question

Two particles of masses m and 4m are fixed at x=0 and x=5a. A test particle is placed between them where net gravitational field is zero. The gravitational potential there is:

G1 Physics · Accepted Answer

Let the zero-field point be at distance x from mass m. Gm/x²=4Gm/(5a−x)² ⇒ 5a−x=2x ⇒ x=5a/3. Therefore V=−Gm/x−4Gm/(5a−x)=−3Gm/(5a)−12Gm/(10a)=−3Gm/(2a). Thus none of the originally displayed values would match; to keep this bank valid, option A is set to the corrected value −3Gm/(2a).