Class 10 Science | Height and acceleration due to gravity

Activity 7.4

Method

Look at the figure of the Earth with points marked at distances R, 2R, 3R and 4R from its center.
Note that at d = R from the center, which is the surface, the acceleration due to gravity is \( g_1 = \frac{GM}{d^2} = 9.8\ \text{m/s}^2 \).
Study how the value at d = 2R has been calculated in the table.
In the same way, calculate the acceleration due to gravity at d = 3R and d = 4R and write the values in the empty cells of the table.
Compare how the values of the acceleration due to gravity change as the distance from the center of the earth goes on increasing.

Distance from the center of the earth (d)	d = 2R	d = 3R	d = 4R
Acceleration due to gravity \( g_1 = \frac{GM}{d^2} \)	\( g_1 = \frac{GM}{(2R)^2} = \frac{1}{4} \times 9.8 = 2.45\ \text{m/s}^2 \)

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