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Question

Acceleration due to gravity is '$$g$$' on the surface of the earth. The value of acceleration due to gravity at a height of $$32 \ km$$ above earth's surface is (Radius of the earth $$=6400 \ km$$)

A
$$0.8 \ g$$
B
$$0.9 \ g$$
C
$$0.99 \ g$$
D
$$1.01 \ g$$
Solution
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Correct option is B. $$0.99 \ g$$
$$h= 32 \ km, R=6400 \ km, $$ so $$h<<R$$

$$g'= g\bigg( 1- \dfrac{2h}{R} \bigg) = g \bigg(1- \dfrac{2 \times 32}{6400} \bigg) $$

$$\implies g'= \dfrac{99}{100} g= 0.99 \ g$$

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