A particle is projected vertically upwards from the surface of the earth (radius `R_(e)`) with a speed equal to one fourth of escape velocity. What is the maximum height attained by it from the surface of the earth ?

Options

A. `(16)/(15)R_(e)`
B. `(R_(e))/(15)`
C. `(4)/(15)R_(e)`
D. None of these

Answer

B

Explanation

From conservation of mechanical energy,
`(1)/(2)mv^(2)=("GMm")/(R_(e))-("GMm")/("R")`
Where R = maximum distance from centre of the earth Also `v=(1)/(4)v_(e)=(1)/(4)sqrt((2"GM")/(R_(e))`
`implies(1)/(2)mxx(1)/(16)xx(2"GM")/(R_(e))=("GMm")/(R_(e))-("GMm")/(R_(e))impliesR=(16)/(15)`
`R_(e)impliesh=R-R_(e)=(R_(e))/(15)`