Escape velocity from a planet is ve. If its mass is increased to 8 times and its radius is increased to2 times, then the new escape velocity would be :

Question

Escape velocity from a planet is ve. If its mass is increased to 8 times and its radius is increased to2 times, then the new escape velocity would be : (A)  ve.  (B)  √2ve.  (C)  2ve.  (D)  2√2ve.

Tardigrade Admin · Accepted Answer

Escape velocity ve=(√2GMe/Re) New escape velocity ve'=(√2G(8Me)/Re) =2(√2GMe/Re)=2ve

Q. Escape velocity from a planet is $v_{e .}$ If its mass is increased to 8 times and its radius is increased to2 times, then the new escape velocity would be :

$v_{e .}$

$2 v_{e .}$

$2 v_{e .}$

$22 v_{e .}$

Escape velocity $v_{e} = \frac{2 G M _{e}}{R _{e}}$ New escape velocity $v_{e}^{^{'}} = \frac{2 G ( 8 M _{e} )}{R _{e}}$ $= 2 \frac{2 G M _{e}}{R _{e}} = 2 v_{e}$

Q. Escape velocity from a planet is ve.​ If its mass is increased to 8 times and its radius is increased to2 times, then the new escape velocity would be :

ve.​

2​ve.​

2ve.​

22​ve.​

Escape velocity ve​=Re​2GMe​​​ New escape velocity ve′​=Re​2G(8Me​)​​ =2Re​2GMe​​​=2ve​

Q. Escape velocity from a planet is $v_{e .}$ If its mass is increased to 8 times and its radius is increased to2 times, then the new escape velocity would be :

$v_{e .}$

$2 v_{e .}$

$2 v_{e .}$

$22 v_{e .}$

Escape velocity $v_{e} = \frac{2 G M _{e}}{R _{e}}$ New escape velocity $v_{e}^{^{'}} = \frac{2 G ( 8 M _{e} )}{R _{e}}$ $= 2 \frac{2 G M _{e}}{R _{e}} = 2 v_{e}$