Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

At what height from the surface of the earth, are the gravitation potential and the value of $g$ are: $-5.4 \times 10^7 \text{ J/kg}$ and $6.0 \text{ ms}^{-2}$ respectively? (Take, the radius of the earth as $6400 \text{ km}$ )

1600 km

1400 km

2000 km

2600 km

Step-by-Step Solution

Formulas:

Gravitational Potential at a distance $r$ from the center ( $r = R+h$ ) is $V = -\frac{GM}{r}$ .
Acceleration due to gravity at distance $r$ is $g_h = \frac{GM}{r^2}$ .

Relation: Dividing the magnitude of potential by the acceleration yields the distance $r$ : $\frac{|V|}{g_h} = \frac{GM/r}{GM/r^2} = r$
Calculation: $r = \frac{5.4 \times 10^7 \text{ J/kg}}{6.0 \text{ ms}^{-2}} = 0.9 \times 10^7 \text{ m} = 9 \times 10^6 \text{ m}$ Converting to kilometers: $r = 9000 \text{ km}$ .
Find Height ( $h$ ): $h = r - R = 9000 \text{ km} - 6400 \text{ km} = 2600 \text{ km}$

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