The escape velocity of a body from the earth' | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The escape velocity from the surface of the earth is given by $v_e = \sqrt{\frac{2GM}{R}}$.At a height $h = R$ from the surface,the distance from

Vedclass · Accepted Answer

$\frac{v_e}{\sqrt{2}}$

Vedclass · Answer

(A) The escape velocity from the surface of the earth is given by $v_e = \sqrt{\frac{2GM}{R}}$.At a height $h = R$ from the surface,the distance from the center of the earth is $r = R + h = R + R = 2R$.The escape velocity $v'$ at this height is given by $v' = \sqrt{\frac{2GM}{r}} = \sqrt{\frac{2GM}{2R}}$.Simplifying this,we get $v' = \sqrt{\frac{1}{2} \cdot \frac{2GM}{R}} = \frac{1}{\sqrt{2}} \sqrt{\frac{2GM}{R}}$.Substituting $v_e$ into the equation,we get $v' = \frac{v_e}{\sqrt{2}}$.

The escape velocity of a body from the earth's surface is $v_e$. The escape velocity of the same body from a height equal to $R$ from the earth's surface will be

Similar Questions

$A$ ball $A$ of mass $m$ falls to the surface of the earth from infinity. Another ball $B$ of mass $2m$ falls to the earth from a height equal to six times the radius of the earth. The ratio of the velocities of $A$ and $B$ on reaching the earth is:

Is it necessary to provide an initial speed of $11.2 \, km/s$ to a rocket launched from Earth?

There is no atmosphere on the moon because

$A$ body is projected vertically upwards from the surface of the Earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height $h$ is $....\,S.$

The escape velocity of a projectile from the earth is approximately .......... $km/sec$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module