Question

Q.39 The ratio of escape velocity of a planet to the escape velocity of earth will be:-
Given: Mass of the planet is 16 times mass of earth and radius of the planet is 4 times the radius of earth.
Options \( 1 \cdot 1: \sqrt{2} \)
2. \( 1: 4 \)
3. \( 2: 1 \)
4. \( 4: 1 \)

Answer 1

Escape velocity is given by:

Ve = (2GM÷R)½

M = Mass of Planet (for now it is earth)

R = Radius of Planet 

For Earth, Ve = Ve  

For Planet, V_ep= (2G*16M÷4R)½

      = 2(2GM÷R)½

      = 2V_e

Thus V_ep ÷ V_e = 2÷1

Therefore 2:1

Answer 2

We know that, escape velocity V_e = \(\sqrt{2gRe}\)

\(V_e∝\sqrt{Re}\)

\(\frac{V_ep}{V_{eRe}}=\sqrt{\frac{4Re}{Re}}\)

\(\frac{V_eP}{V_{eRe}}=\frac{2}{1}\)