Calculate the value of g at a height of 3600 km above the surface of the Earth. Ans. (4.0 ms⁻²)
Given:
Height above the Earth's Surface = h = 3600 km = 3.6 x 10³x 10³ m = 3.6 x 10⁶ m
∴ Mass of the Earth = Mₑ = 6 x 10²⁴ kg
∴ Radius of the Earth = Rₑ = 6.4 x 10⁶ m
∴ Gravitational Constant = G = 6.67 x 10⁻¹¹N m² kg⁻²
To Find:
Value of Gravitational acceleration at height 3600 km above the Earth's surface = g = ? m s⁻²
Solution:
Let a body of mass m is placed at height h above the surface of the Earth So The distance between the centres of the body and the Earth = r = (Rₑ + h)
According to the Law of Gravitation's, we have
F = GmMₑ(Rₑ+h)2 -----eqn (1)
But according to the 2nd law of Newton
F = W = mg ----eqn (2)
By comparing these two Eqns 1 & 2 we have
mg = GmMₑ(Rₑ+h)2
m will cancel from both sides hence
g = GMₑ(Rₑ+h)2
putting values
g = 6.67x10⁻¹¹Nm²kg⁻²x6x10²⁴ kg(3.6 x 10⁶m+ 6.4x 10⁶ m)2
g = 6.67x10⁻¹¹Nm²kg⁻²x6x10²⁴ kg(10x 10⁶ m)2
g = 6.67x10⁻¹¹Nm²Kg⁻²x6x10²⁴ kg(100x 10¹² m2}
g = 6.67x6100x 10⁻¹¹⁺²⁴⁻¹² m s⁻²
by simplifying we get
g = 0.4003x 10¹ m s⁻²
g = 4.003x 10⁻¹ x 10¹ m s⁻²
g = 4.003x 10⁻¹⁺¹ m s⁻²
or
g = 4.003x10⁰ m s⁻²
g = 4.0 m s⁻²
Thus, the gravitational acceleration g on the above surface of Earth at height 3600 Km is 4.0 ms⁻²
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© 2020-21 Academic Skills and Knowledge (ASK)
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