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Q.

Is it true that at a height equal to the earth's radius, the value of g becomes 1/4th of its value

on the earth?

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a

True

b

False

answer is A.

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Detailed Solution

The above statement is true.
The acceleration due to gravity on the surface of the earth is given by
g1 =

\frac{GM}{R^{2}}

g1 = gravity acceleration
G = gravitational constant
R = Radius of the earth
M = mass of the earth
g is the gravitational acceleration at height H = R from the surface of the earth.
g2 =

\frac{GM}{(R + H)^{2}}

\Rightarrow

g2 =

\frac{GM}{(R + R)^{2}}

\Rightarrow

g2 =

\frac{g_{1}}{4}

At the height equal to the earth’s radius above the surface, the acceleration due to gravity will be 1/4th of its value on the surface of the earth is equal to “R”(radius of the earth).

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