If the gravitational field in space is given as -K/r². Taking the reference point to be at r = 2 cm with gravitational potential V = 10 J kg⁻¹, find the gravitational potential at r = 3 cm in SI unit. [K = 6 J cm kg⁻¹]
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Question

If the gravitational field in space is given as -K/r². Taking the reference point to be at r = 2 cm with gravitational potential V = 10 J kg⁻¹, find the gravitational potential at r = 3 cm in SI unit. [K = 6 J cm kg⁻¹]

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G1 Physics · Accepted Answer

Gravitational field g(r) = −dV/dr = −K/r², hence dV/dr = K/r². Integrating from r=2 cm, V=10 to r=3 cm gives V−10 = K(1/2 − 1/3) = 6×(1/6)=1. Therefore V = 11 J kg⁻¹.

If the gravitational field in space is given as −K/r². Taking the reference point to be at r = 2 cm with gravitational potential V = 10 J kg⁻¹, find the gravitational potential at r = 3 cm in SI unit. [K = 6 J cm kg⁻¹]