(A) The formula for escape velocity is $v_{e} = \sqrt{\frac{2GM}{R}}$.For Planet $A$,the escape velocity is $v_{A} = \sqrt{\frac{2GM}{R}}$.For Planet

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(A) The formula for escape velocity is $v_{e} = \sqrt{\frac{2GM}{R}}$.For Planet $A$,the escape velocity is $v_{A} = \sqrt{\frac{2GM}{R}}$.For Planet $B$,the mass is $M' = \frac{M}{2}$ and the radius is $R' = \frac{R}{2}$.Thus,the escape velocity for Planet $B$ is $v_{B} = \sqrt{\frac{2G(M/2)}{R/2}} = \sqrt{\frac{2GM}{R}}$.Comparing the two,we get $\frac{v_{A}}{v_{B}} = \frac{\sqrt{2GM/R}}{\sqrt{2GM/R}} = 1$.Given that $\frac{v_{A}}{v_{B}} = \frac{n}{4}$,we have $1 = \frac{n}{4}$,which implies $n = 4$.

Class 11 Physics Gravitation Escape Velocity and Escape Energy

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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

JEE MAIN 2020 All JEE MAIN

A
$4$
B
$1$
C
$2$
D
$3$

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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

Similar Questions

The escape velocity of an object from the Earth depends upon the mass of the Earth $(M)$,its mean density $(\rho)$,its radius $(R)$,and the gravitational constant $(G)$. Thus,the formula for escape velocity is:

The radius and mean density of a planet are four times that of the Earth. The ratio of the escape velocity on the Earth to the escape velocity on the planet is:

The escape velocity of a sphere of mass $m$ is given by ($G =$ Universal gravitational constant; $M_e =$ Mass of the earth and $R_e =$ Radius of the earth).

If the radius of a planet is $R$ and its density is $\rho$,the escape velocity from its surface will be

$A$ rocket is fired vertically with a speed of $4 \ km/s$ from the Earth's surface. How far from the Earth does the rocket go before returning to the Earth (in $km$)? (Take radius of Earth $R = 6.4 \times 10^6 \ m$ and $g = 10 \ m/s^2$)

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