From what height above the surface of the earth should an object be dropped to initially have an acceleration of 0.54g? (G = 6.67 × 10^-11 N ∙ m²/kg²,M_earth = 5.97 × 10²⁴ kg,R_earth = 6.38 × 10⁶ m) A)2300 km B)1700 km C)5400 km D)2900 km

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Quizplus · Accepted Answer

The acceleration due to gravity at a height h above the surface of the Earth is given by:$$g' = \frac{GM_e}{(R_e + h)^2}$$where G is the gravitational constant, M_e is the mass of the Earth, and R_e is the radius of the Earth.We want to find the height h at which g' = 0.54g. Substituting the given values into the equation, we get:$$0.54g = \frac{GM_e}{(R_e + h)^2}$$Solving for h, we get:$$h = \frac{GM_e}{0.54gR_e^2} - R_e$$Plugging in the given values, we get:$$h = \frac{(6.67 	imes 10^{-11} N \cdot m^2/kg^2)(5.97 	imes 10^{24} kg)}{(0.54)(9.81 m/s^2)(6.38 	imes 10^6 m)^2} - 6.38 	imes 10^6 m$$$$h = 2300 km$$Therefore, the correct answer is A.

From What Height Above the Surface of the Earth Should