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Question

A particle is projected vertically upwards from the surface of the earth (radius R) with a speed equal to one-fourth of escape velocity. The maximum height attained by it from the surface of the earth is

A
R5
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B
R10
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C
R15
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D
R20
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Solution

The correct option is C R15
Escape velocity, ve=2gR
v=2gR4=gR22
From conservation of energy
12mv2GMmR=0GMmR+h

Using g=GMR2
12mgR8 mg R=gR2mR+h
116=1RR+h
116=hR+h
R+h=16h
R=15h
h=R15

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