Question

At what altitude above the earth’s surface would the acceleration due to gravity be 4.9m/s2? Assume the radius of the earth is 6.4 x 10 raise to power 6 m and the acceleration due to gravity on the surface of the earth is 9.8m/s2

Answer 1

Answer on Question #55222-Physics-Mechanics-Kinematics-Dynamics

At what altitude above the earth's surface would the acceleration due to gravity be 4.9ms-2? Assume the mean radius of the earth is $6.4 \times 106$ meters and the acceleration due to gravity 9.8ms-2 on the surface of the earth.

Solution

The velocity of a freely falling body increased at a steady rate i.e., the body had acceleration.

This acceleration is called acceleration due to gravity $g$ .

Let a body of mass $m$ be placed on the surface of the Earth:

$$g = \frac {G M}{R ^ {2}}.$$

where $M$ is the mass of the Earth, $R$ is the radius of the Earth and $G$ is the gravitational constant.

Let the body be now placed at a height $h$ above the Earth's surface. Let the acceleration due to gravity at that position be $g'$ .

Then,

$$g ^ {\prime} = \frac {G M}{(R + h) ^ {2}}$$

For comparison, the ratio between $g'$ and $g$ is taken

$$\frac {g ^ {\prime}}{g} = \left(\frac {R}{R + h}\right) ^ {2}$$

Thus,

$$h = R \left(\sqrt {\frac {g}{g ^ {\prime}}} - 1\right) = 6. 4 \cdot 1 0 ^ {6} \cdot \left(\sqrt {\frac {9 . 8}{4 . 9}} - 1\right) = 2. 6 5 \cdot 1 0 ^ {6} m$$

Answer: $2.65 \cdot 10^{6} m$

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