Compare escape speeds of two planets of masses M and 4M and radii 2R and R respectively.
Answers
We have to compare the escape speeds of two planets of masses M and 4M and radii 2R and R respectively.
solution : escape speed of the planet is given by, v = √{2GM/R}
where M is mass of planet, G is gravitational constant and R is radius of it.
case 1 : mass of planet, M₁ = M
radius of planet, R₁ = 2R
so, v₁ = √{2GM₁/R₁}
= √{2GM/2R}
= √{GM/R} ....(1)
case 2 : mass of planet, M₂ = 4M
radius of planet, R₂ = R
so, v₂ = √{2G(4M)/R}
= 2√2 [√{GM/R} ]
from equation (1) ,
v₂ = 2√2v₁
Therefore escape velocity of 2nd planet is 2√2 time of escape velocity of 1st planet.
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