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

Question

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

Tardigrade Admin · Accepted Answer

Ve=√(2 G Me/Re) Mp=(Me/2), Rp=(Re/4) V'e=√(2 G Me × 4/2 Re)=√2 Ve

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

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

$2 v_{e}$

$2 v_{e}$

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

$V_{e} = \frac{2 G M _{e}}{R _{e}}$
$M_{p} = \frac{M _{e}}{2}, R_{p} = \frac{R _{e}}{4}$
$V_{e}^{'} = \frac{2 G M _{e} \times 4}{2 R _{e}} = 2 V_{e}$

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

2​ve​​

2​ve​

2ve​

2ve​​

Ve​=Re​2GMe​​​ Mp​=2Me​​,Rp​=4Re​​ Ve′​=2Re​2GMe​×4​​=2​Ve​

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

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

$2 v_{e}$

$2 v_{e}$

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

$V_{e} = \frac{2 G M _{e}}{R _{e}}$
$M_{p} = \frac{M _{e}}{2}, R_{p} = \frac{R _{e}}{4}$
$V_{e}^{'} = \frac{2 G M _{e} \times 4}{2 R _{e}} = 2 V_{e}$