Question

Two planets and have the same material density. If the radius of is twice that of then the ratio of the escape velocity is:

Answer 1

If the radius of is twice that of then the ratio of the escape velocity is 2

1. The formula of escape velocity is given by
2. $V=\sqrt{\frac{2GM}{R} }$ here V is the escape velocity , G is gravitational constant,M is the mass and R is the radius.
3. The formula for the escape velocity in terms of material density is
4. $V=\sqrt{8G\pi p}R$ where p is the material density
5. Now let us assume planet 1 with radius is R then radius of planet 2 is 2r
6. Then the ratio if there escape velocity is
7. $\frac{V2}{V1}=\frac{R2}{R1}=\frac{2R}{R}=2$