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 increases to ten times is

• A. 8
• B. 64
• C. 640
• D. 4800

Answer 1

The correct option is B 64

The escape velocity of any planatery system is

$V=\sqrt{\frac{2GM}{R}}$

Where M= mass of the planet

R=Radius of earth.

$V_1=\sqrt{\frac{2GM}{6400}}$

But for $V_2=10V_1$

$\sqrt{\frac{2GM}{R_2}}$=$\sqrt{\frac{2GM}{6400}}$

$V_2=64km$