ICSE Class 10 Answered
What is the Escape Velocity?
Asked by preranapatil4360 | 25 Dec, 2021, 19:55: PM
Escape velocity is defined as minimum velocity required for a particle at the surface of planet
so that the particle reaches a far point away from planet where the gravitational force of attraction
acting on the particle is zero .
Let us consider the escape velocity requirement of a particle on earth's surface
On surface of earth , let us consider the particle is projected with speed v upwards.
Total energy on surface of earth = Kinetic energy + Potential energy
Total energy on surface of earth = (1/2) m v2 - ( G M m ) / R ....................................(1)
where m is mass of particle. Second term in above expression is potential energy ,
where G is universal gravitational constant ,M is mass of earth and R is radius of earth .
At far away point ( at infinity ) , potential energy is zero and let us consider the speed is negligible
compare to initial speed at earth's surface
Hence at infinity , total energy is zero
Hence by conservation of energy , (1/2) m v2 - ( G M m ) / R = 0
After simplification , above expression becomes
![begin mathsize 14px style v space equals space square root of 2 space G M over R space end root space equals space square root of 2 space open parentheses fraction numerator G M over denominator R squared end fraction close parentheses R end root space equals space square root of 2 space g space R end root end style](https://images.topperlearning.com/topper/tinymce/cache/8164e0831b8afbe55eb97fc0fc0027e3.png)
Where g = G M / R2 , is the acceleration due to gravity on earth surface
if we substitute R = 6378 km in above expression , we get
![begin mathsize 14px style v space equals space square root of 2 space g space R end root space space equals space square root of 2 cross times 9.8 cross times 6378 cross times 1000 end root space space equals space 1.118 space cross times space 10 to the power of 4 space m divided by s end style](https://images.topperlearning.com/topper/tinymce/cache/9ce839a598fe043b6d395b5295a4b7e0.png)
Hence escape velocity on earth's surface = 11.18 km/s
Answered by Thiyagarajan K | 25 Dec, 2021, 21:54: PM
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