A planet has mass 16Mₑ and radius 4Rₑ, where Mₑ and Rₑ are the mass and radius of Earth. The ratio of its escape speed to Earth's escape speed is:
Options

Question

A planet has mass 16Mₑ and radius 4Rₑ, where Mₑ and Rₑ are the mass and radius of Earth. The ratio of its escape speed to Earth's escape speed is:

G1 Physics · Accepted Answer

Escape speed is v = √(2GM/R) For the planet: vₚ = √[2G(16Mₑ)/(4Rₑ)] For Earth: vₑ = √(2GMₑ/Rₑ) Therefore, vₚ/vₑ = √(16/4) = 2 So, vₚ : vₑ = 2 : 1 The source page shows an inconsistent option label, but the worked calculation gives 2 : 1. Hence option B follows.