Question

The radius in kilometers to which the present radius of the earth (R = 6400 km) is to be compressed so that the escape velocity is increased 10 times is ______.

Options

• 61

• 62

• 63

• 64

Answer 1

The radius in kilometers to which the present radius of the earth (R = 6400 km) is to be compressed so that the escape velocity is increased 10 times is 64.

Explanation:

Escape velocity,

`ν_e = sqrt((2GM)/R)`

Let R' be the radius so that escape velocity is increased 10 times.

`ν^' = 10ν_e = sqrt((2GM)/R^')`

⇒ `10 xx sqrt((2GM)/R) = sqrt((2GM)/R^')`

∴ `R^' = R/100 = 6400/100 = 64` km