Question

The radius in kilometers to which the present radius of the earth (R 6400 km) is to be compressed so that the escapo velocity is increases to ten times is

Answer 1

Formula for the escape velocity is (2GM/r)^1/2

Let escape velocity of earth be v with radius r

Now new escape velocity is 10v with radius r1

Dividing new velocity by previous velocity

i.e. 1/10=(r1/r)^1/2

1/100=r1/r

1/100=r1/6400   (radius of earth = 6400)

r1=64km