Gravitation Question 355
A shell is fired vertically from the earth with speed $ \frac{V_{esc}}{N} $, where N is some number greater than one and $ V_{esc} $ is escape speed for the earth. Neglecting the rotation of the earth and air resistance, the maximum altitude attained by the shell will be one radius of the earth)
Options:
A) $ [\frac{N^{2}{R_{E}}}{N^{2}-1}] $
B) $ [\frac{N R_{E}}{N^{2}-1}] $
C) $ [\frac{{R_{E}}}{N^{2}-1}] $
D) $ [\frac{{R_{E}}}{N^{2}}] $
Show Answer
Answer:
Correct Answer: C
Solution:
-
By the conservation of energy
$ [-\frac{GMm}{R_{E}}\text{+}\frac{1}{2}\frac{m}{N^{2}}\frac{GM}{2R_{E}}\text{=-}\frac{GMm}{H}] $
$ [\Rightarrow H=\frac{N^{2}R_{E}}{N^{2}-1}] $
Altitude $ [=H-R=\frac{R_{E}}{N^{2}-1}] $
BETA
