The escape velocity from the surface of the earth is 11.2 km s-1 . What is the escape velocity in a planet whose radius is three times that of the earth and on which the acceleration due to gravity is three times of that on the earth?

Question

The escape velocity from the surface of the earth is 11.2 km s-1 . What is the escape velocity in a planet whose radius is three times that of the earth and on which the acceleration due to gravity is three times of that on the earth? (A)  11.2 km s-1  (B)  22.4 km s-1  (C)  33.6 km s-1  (D)  5.6 km s-1

Tardigrade Admin · Accepted Answer

Escape speed on the earth surface ve=√2 ge Re 11.2=√2 ge Re . . (i) Escape speed on the planet surface vp=√2 gp Rp =√2(3 ge)(3 Re) [∵ gp=3 ge Rp=3 Re] =3 √2 ge Re Vp=3 Ve=33.6 m / s

Q. The escape velocity from the surface of the earth is $11.2 km s^{- 1}$ . What is the escape velocity in a planet whose radius is three times that of the earth and on which the acceleration due to gravity is three times of that on the earth?

$11.2 km s^{- 1}$

$22.4 km s^{- 1}$

$33.6 km s^{- 1}$

$5.6 km s^{- 1}$

Escape speed on the earth surface $v_{e} = 2 g_{e} R_{e}$
$11.2 = 2 g_{e} R_{e} ..$ (i)
Escape speed on the planet surface
$v_{p} = 2 g_{p} R_{p}$
$= 2 (3 g_{e}) (3 R_{e})$
$[∵ g_{p} = 3 g_{e} R_{p} = 3 R_{e}]$
$= 3 2 g_{e} R_{e}$
$V_{p} = 3 V_{e} = 33.6 m / s$

Q. The escape velocity from the surface of the earth is 11.2kms−1 . What is the escape velocity in a planet whose radius is three times that of the earth and on which the acceleration due to gravity is three times of that on the earth?

11.2kms−1

22.4kms−1

33.6kms−1

5.6kms−1