Question

Find the height at which g become 1/3 of g at the surface? (Radius of earth is

=6400km)​

Answer 1

Answer:

6472 km

Explanation:

Value of g at a height h is

g' = gR² / (R + h)²

In the g' = g / 3

So by equating both sides we get,

g / 3 = gR² / (R + h)²

Cutting off the common g from both sides

1 / 3 = R² / (R + h)²

By cross multiplying we get

(R + h)² = 3R²

R + h = √3 R

Bringing the R from left to right. While bringing it will become -R

h = (√3 - R) R

Taking the common R outside

h = (√3 - 1) R

we know that the value of R = 6400 km

By putting the values we get

h = (1.73 - 1) x 6400

  = 0.73 x 6400

  = 6472 km

The answer is 6472 km.

Hope this will be very helpful.