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At what height from the surface of earth the gravitation potential and the value of g are -5.4×10⁷ J kg⁻¹ and 6.0 m s⁻² respectively? Take the radius of earth as 6400 km.

Asked in NEET 2016 Phase-I · Variation with height

Answer: (3) 2600 km

Step-by-step solution

At a height h the potential is Vₕ=-(GM)/(R+h) and gravity is gₕ=(GM)/((R+h)²).

Dividing one by the other makes GM cancel: (Vₕ)/(gₕ)=-(R+h).

R+h=-(-5.4×10⁷)/(6.0)=9×10⁶ m.

Subtracting the earth's radius, h=9×10⁶-6.4×10⁶=2.6×10⁶ m.

h=2600 km.

Why the other options are wrong

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