The escape velocity for the earth is ve. The escape velocity for a planet whose radius is (1/4)th, the radius of the earth and mass half that of the earth is

Question

The escape velocity for the earth is ve. The escape velocity for a planet whose radius is (1/4)th, the radius of the earth and mass half that of the earth is (A) (ve/√2) (B) √2ve (C) 2ve (D) (ve/2)

Tardigrade Admin · Accepted Answer

Escape velocity of a body from the surface of the earth is given by

v_{e} = \frac{2 G M _{e}}{R _{e}}

...(i)
So, according to the question,

M_{P} = \frac{M _{e}}{2} and R_{P} = \frac{R _{e}}{4}

Now, escape velocity of a body from the surface of the planet is given by

v_{P} = \frac{2 G M _{P}}{R _{P}}

or

V_{P} = \frac{2 G \times M _{e} \times 4}{2 R _{e}} = 2 \frac{2 G M _{e}}{R _{e}}

= 2 v_{e}

[from Eq.(i)]

Q. The escape velocity for the earth is $v_{e}$ . The escape velocity for a planet whose radius is $\frac{1}{4} t h$ , the radius of the earth and mass half that of the earth is

$\frac{v _{e}}{2}$

$2 v_{e}$

$2 v_{e}$

$\frac{v _{e}}{2}$

Q. The escape velocity for the earth is ve​. The escape velocity for a planet whose radius is 41​th, the radius of the earth and mass half that of the earth is

2​ve​​

2​ve​

2ve​

2ve​​

Q. The escape velocity for the earth is $v_{e}$ . The escape velocity for a planet whose radius is $\frac{1}{4} t h$ , the radius of the earth and mass half that of the earth is

$\frac{v _{e}}{2}$

$2 v_{e}$

$2 v_{e}$

$\frac{v _{e}}{2}$