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 (VA/VB) is

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 (VA/VB) is (A) 2 (B)  √2  (C)  (1/√2)  (D)  (1/2)

Tardigrade Admin · Accepted Answer

Escape velocity is given by ve=√(2GM/R)=√(2G/R)× (4/3)π R3ρ ⇒ ve=R√(8/3)π Gρ ∴ (vA/vB)=(RA/RB)=2

Q. 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 $\frac{V _{A}}{V _{B}}$ is

2

$2$

$\frac{1}{2}$

$\frac{1}{2}$

Escape velocity is given by $v_{e} = \frac{2 GM}{R} = \frac{2 G}{R} \times \frac{4}{3} π R^{3} ρ$ $\Rightarrow$ $v_{e} = R \frac{8}{3} π Gρ$ $∴$ $\frac{v _{A}}{v _{B}} = \frac{R _{A}}{R _{B}} = 2$

Q. 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 VB​VA​​ is

2

2​

2​1​

21​

Escape velocity is given by ve​=R2GM​​=R2G​×34​πR3ρ​ ⇒ ve​=R38​πGρ​ ∴ vB​vA​​=RB​RA​​=2

Q. 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 $\frac{V _{A}}{V _{B}}$ is

$2$

$\frac{1}{2}$

$\frac{1}{2}$

Escape velocity is given by $v_{e} = \frac{2 GM}{R} = \frac{2 G}{R} \times \frac{4}{3} π R^{3} ρ$ $\Rightarrow$ $v_{e} = R \frac{8}{3} π Gρ$ $∴$ $\frac{v _{A}}{v _{B}} = \frac{R _{A}}{R _{B}} = 2$