Planet A has mass M and radius R. Planet B has half the mass and half the radius of Planet A. If the escape velocities from the Planets A and B are vA and vB, respectively, then (vA/vB)=(n/4). The value of n is :

Question

Planet A has mass M and radius R. Planet B has half the mass and half the radius of Planet A. If the escape velocities from the Planets A and B are vA and vB, respectively, then (vA/vB)=(n/4). The value of n is : (A) 3 (B) 1 (C) 2 (D) 4

Tardigrade Admin · Accepted Answer

Ve = √(2GM/R) (Escape velocity) VA = √(2GM/R) VB = √(2G[M/ 2]/R/ 2) = √(2GM/R) (VA/VB) = 1 = (n/4) ⇒ n = 4

Q. Planet $A$ has mass $M$ and radius $R$ . Planet $B$ has half the mass and half the radius of Planet $A$ . If the escape velocities from the Planets $A$ and $B$ are $v_{A}$ and $v_{B}$ , respectively, then $\frac{v _{A}}{v _{B}} = \frac{n}{4}$ . The value of $n$ is :

$3$

$1$

$2$

$4$

$V_{e} = \frac{2 GM}{R}$ (Escape velocity)
$V_{A} = \frac{2 GM}{R}$
$V_{B} = \frac{2 G [ M /2 ]}{R /2} = \frac{2 GM}{R}$
$\frac{V _{A}}{V _{B}} = 1 = \frac{n}{4} \Rightarrow n = 4$

Q. Planet A has mass M and radius R. Planet B has half the mass and half the radius of Planet A. If the escape velocities from the Planets A and B are vA​ and vB​, respectively, then vB​vA​​=4n​. The value of n is :

3

1

2

4

Ve​=R2GM​​ (Escape velocity) VA​=R2GM​​ VB​=R/22G[M/2]​​=R2GM​​ VB​VA​​=1=4n​⇒n=4

Q. Planet $A$ has mass $M$ and radius $R$ . Planet $B$ has half the mass and half the radius of Planet $A$ . If the escape velocities from the Planets $A$ and $B$ are $v_{A}$ and $v_{B}$ , respectively, then $\frac{v _{A}}{v _{B}} = \frac{n}{4}$ . The value of $n$ is :

$3$

$1$

$2$

$4$

$V_{e} = \frac{2 GM}{R}$ (Escape velocity)
$V_{A} = \frac{2 GM}{R}$
$V_{B} = \frac{2 G [ M /2 ]}{R /2} = \frac{2 GM}{R}$
$\frac{V _{A}}{V _{B}} = 1 = \frac{n}{4} \Rightarrow n = 4$