Gravitation Question 132

Question: A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is [KCET (Engg./Med.) 2002]

Options:

A) R/3

B) R/2

C) R/4

D) R/5

Show Answer

Answer:

Correct Answer: A

Solution:

If body is projected with velocity v $ [(v<v_{e})] $ then height up to which it will rise, $ [h=\frac{R}{\frac{v_{e}^{2}}{v^{2}}-1}] $ $ [v=\frac{v_{e}}{2}] $ (given) \ $ [h=\frac{R}{{{\left( \frac{v_{e}}{v_{e}/2} \right)}^{2}}-1}=\frac{R}{4-1}=\frac{R}{3}] $



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