Gravitation Question 355

Question: A shell is fired vertically from the earth with speed $ [\frac{V_{esc}}{N},] $ where Nis some number greater than one and V is escape speed for the earth. Neglecting the nation of the earth and air resistance, the maximum altitude attained by the shell will be is 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 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}] $



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