Question

Two planets A and B have the same material density. If the radius of A is twice that of B, then the ratio of escape velocity `"V"_"A"/"V"_"B"` is ______.

Options

• 2

• `sqrt2`

• `1/sqrt2`

• `1/2`

Answer 1

Two planets A and B have the same material density. If the radius of A is twice that of B, then the ratio of escape velocity `"V"_"A"/"V"_"B"` is 2.

Explanation:

v_e = `sqrt((2 "GM")/"R")`

= `sqrt((2"G")/"R" xx 4/3 π"R"^3ρ)`

`"v"_"e" ∝ "R"`

`"V"_"A"/"V"_"B" = "R"_"A"/"R"_"B" = 2/1`