Question

At what height 'h' the value of 'g' will be half of that on the surface of earth

Answer 1

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Answer 2

Answer:

2650 km

Explanation:

At a height ‘h’

g' = g [R / R + h]²

In the question, g' = half the value = g / 2

g / 2 = g [ R / R + h]²

g is common on both side. So we can cancel it.

1 / 2 = [R / R + h]²

1 / √2 = R / R + h

By cross multiplying we get,

R + h = √2 R

Then take R in left to right. While bringing to right side, it will become -R.

h = (√2 -  R ) R

Taking R outside.

h = (√2 -  1) R

We know that R = 6400 km

By putting the values, we get

h = (1.414−1) x 6400

  = 2649.6

By rounding off we get,

h = 2650 km

The answer is 2650 km

Hope this is helpful.