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CONCEPT:
- Gravitational acceleration: It is the acceleration gained by an object due to gravitational force.
- Its SI unit is m/s2.
- It has both magnitude and direction, hence, it’s a vector quantity.
- Acceleration due to gravity is represented by g.
- The standard value of g on the surface of the earth at sea level is 9.8 m/s2.
Acceleration due to gravity on the surface is given:
g1 = GM/R2
Acceleration due to gravity above the surface is given:
g2 = GM/(R + H)2
Where, R = Radius of the earth (6400 km), and H = height in meters
CALCULATION:
From the above discussion it's clear that
\(\frac{{{g_2}}}{{{g_1}}} = \frac{{GM/{{(R + H)}^2}}}{{GM/{R^2}}}\)
\(\frac{{{g_2}}}{{{g_1}}} = \frac{{{R^2}}}{{{{(R + H)}^2}}}\)
\(\frac{{{g_2}}}{{9.8}} = \frac{{{{(6.4 \times {{10}^6})}^2}}}{{{{(6.4 \times {{10}^6} + 0.01 \times {{10}^6})}^2}}}\)
g2 = 9.77 m/s2
The correct option is 9.77 m/s2
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