A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 km s- 1 , the escape velocity from the surface of the planet would be

Question

A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 km s- 1 , the escape velocity from the surface of the planet would be (A) 0.11kms- 1 (B) 1.1 km s- 1 (C) 11 km s- 1 (D) 110 km s- 1

Tardigrade Admin · Accepted Answer

v textescape=√(2 textitGM/ textitR) for the earth ve=11kms- 1 Mass of the planet = 10Me . Radius of the planet = (R/10) . ∴ ve=√(2 textitGM × 1 0/ textitR / text10)= text10× text11=110 text km text s- 1

Q. A planet in a distant solar system is $10$ times more massive than the earth and its radius is $10$ times smaller. Given that the escape velocity from the earth is $11 km s^{- 1}$ , the escape velocity from the surface of the planet would be

$0.11 km s^{- 1}$

$1.1 km s^{- 1}$

$11 km s^{- 1}$

$110 km s^{- 1}$

$v_{escape} = \frac{2 GM}{R}$ for the earth
$v_{e} = 11 km s^{- 1}$
Mass of the planet = $10 M_{e}$ .
Radius of the planet = $\frac{R}{10}$ .
$∴$ $v_{e} = \frac{2 GM \times 10}{R / 10} = 10 \times 11 = 110 km s^{- 1}$

Q. A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11kms−1 , the escape velocity from the surface of the planet would be

0.11kms−1

1.1kms−1

11kms−1

110kms−1