An object is projected vertically upwards from the surface of the earth with a velocity 3 times the escape velocity ve from earth's surface. What will be its final velocity after escape from the earth's gravitational pull?
ve√2
√2ve
2√2ve
2ve
A
2√2ve
B
2ve
C
ve√2
D
√2ve
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Solution
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We know,
Ve (on surface of earth)=√2GMR
Given,
vi=3ve
Let mass of object=m,
Apply energy conservation,
12mvi+−GMmR=12mv2f+0 (as Rfinal=∞)
12m×92GMR−GMmR=12mv2f
8GMmR=12mv2f
vf=√16GMR
vf=√8×√2GMR=√8ve
Hence option B is the correct answer.
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