A spaceship is launched into a circular orbit close to earth's surface. The additional velocity that should be imparted to the spaceship in the orbit to overcome the gravitational pull is: (Radius of earth =6400km and g=9.8ms−1)
A
11.2kms−1
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B
8kms−1
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C
3.2kms−1
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D
1.5kms−1
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Solution
The correct option is C3.2kms−1
Given,
Radius of the earth, R=6400km
Acceleration due to gravity, g=9.8m/s2
When a satellite is orbitting the earth its velocity is its orbital velocity given by orbital velocity: V0=√GMR=√gR[∵g=GMR2]
If it has to overcome gravitational pull then its velocity should be escape velocity escape velocity Ve=√2GMr=√2gR
Additional velocity required is V=Ve−V0=√2gR−√gR=√gR(√2−1)
given that R=64004m=64×106m
g=9.8m/s2
So, additional velocity will be: V=√gR(√2−1)=√9.8×6.4×106(√2−1)