Question

The value of gravitational acceleration g at a height h above the earth's surface is `"g"/4`, then ______. (R = radius of earth)

Options

• h = R

• h = `"R"/2`

• h = `"R"/3`

• h = `"R"/4`

Answer 1

The value of gravitational acceleration g at a height h above the earth's surface is `"g"/4`, then h = R. (R = radius of earth)

Explanation:

The value of acceleration due to gravity g at a height h is given by

g' = g`("R"_"e"/("R"_"e"+"h"))^2`

Here, R_e = radius of earth

g = acceleration due to gravity at earth surface.

g' = `"g"/4` and R_e = R

So, `"g"/4` = g`("R"/("R"+"h"))`

`1/2="R"/("R"+"h")`

⇒ 2R = R + h 

⇒ R = h