Gravitation Question 115
Question: A rocket of mass M is launched vertically from the surface of the earth with an initial speed V. Assuming the radius of the earth to be R and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is [AMU 1995]
Options:
A) $ [R/\left( \frac{gR}{2V^{2}}-1 \right)] $
B)$ [R,\left( \frac{gR}{2V^{2}}-1 \right)] $
C) $ [R/\left( \frac{2gR}{V^{2}}-1 \right)] $
D) $ [R\left( \frac{2gR}{V^{2}}-1 \right)] $
Show Answer
Answer:
Correct Answer: C
Solution:
$ [\Delta K.E.=\Delta U] $ $ [\Rightarrow ,,\frac{1}{2}MV^{2}=GM_{e}M,\left( \frac{1}{R}-\frac{1}{R+h} \right)] $ ?(i) Also $ [g=\frac{GM_{e}}{R^{2}}] $ ?(ii) On solving (i) and (ii) $ [h=\frac{R}{\left( \frac{2gR}{V^{2}}-1 \right)}] $
