Gravitation Question 214
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
Options:
A) $ [R/\left( \frac{gR}{2V^{2}}-1 \right)] $
B) $ [{R_{{}}}\left( \frac{gR}{2V^{2}}-1 \right)] $
C) $ [R/\left( \frac{gR}{2V^{2}}-1 \right)] $
D) $ [R\left( \frac{2gR}{V^{2}}-1 \right)] $
Show Answer
Answer:
Correct Answer: C
Solution:
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$ [\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)}] $
