At what height from the surface of the earth the value of g is 6 m/s^2
Answers
Explanation:
At 1782.35 km km from the surface of earth the value of g is 6 m/s².
Explanation:
The acceleration due to gravity at different altitude is given by the formula:
gh/g = R²/(R + h)²
Where,
gh = Acceleration due to gravity at certain height = 6 m/s²
g = Acceleration due to gravity at earth's surface = 9.8 m/s²
R = Radius of earth = 6400 km
h = Height
On substituting the values, we get,
6/9.8 = (6400)²/(6400 + h)²
0.612 = (40.96 × 10⁶)/((40.96 × 10⁶) + h² + (12.8 × 10³)h)
0.612 × ((40.96 × 10⁶) + h² + (12.8 × 10³)h) = 40.96 × 10⁶
(25.06 × 10⁶) + 0.612h² + (7.83 × 10³)h = 40.96 × 10⁶
0.612h² + (7.83 × 10³)h = (40.96 × 10⁶) - (25.06 × 10⁶)
0.612h² + (7.83 × 10³)h = 15.9 × 10⁶
0.612h² + (7.83 × 10³)h - (15.9 × 10⁶) = 0
On applying quadratic equation given below, we get,
h = (-b ± √(b² - 4ac))/2a
Where,
a = 0.612; b = 7.83 × 10³; c = -(15.9 × 10⁶)
On applying quadratic equation, we get,
h = (-0.612 ± √((0.612)² + (4 × 0.612 × 15.9 × 10⁶)))/(2 × 0.612)
On solving, we get,
h = 1782.35 or −14576.5
The negative acceleration due to gravity is impossible. Thus, h is 1782.35 km.
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