Question

The escape velocity of a body from any planet, whose mass is six times the mass of earth and radius is twice the radius of earth will be
(v₈ = escape velocity of a body from the earth's surface).

Options

• `2sqrt2  "v"_"e"`

• `3/2 "v"_"e"`

• 2v_e

• `sqrt3 "v"_"e"`

Answer 1

`sqrt3 "v"_"e"`

Explanation:

The escape velocity of body from earth's surface is

`"v"_"e" = sqrt("2GM"/"R")`

where, G is universal gravitational constant. M is mass of earth and R is the radius of the earth.

For the planet, M₁ = 6M and R₁ = 2R

∴ The escape velocity from the planet will be

`"v"_"p" = sqrt(("2G"(6"M"))/("2R")) = sqrt3 "v"_"e"`