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  • A projectile is fired from the surface of earth with a velocity <img alt="Kv_{e}\left ( K <1 \right )" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cfn_cm%20Kv_%7Be%7D%5Cleft%20%2

A projectile is fired from the surface of earth with a velocity Kv_{e}\left ( K <1 \right ) where v_{e} is the escape velocity from surface of earth. The maximum height up to which the projectile will rise (from the centre of earth) will be

Option: 1

KR


Option: 2

\left ( K^{2}+1 \right )R


Option: 3

\frac{R}{K^{2}+1}

 


Option: 4

\frac{R}{1-K^{2}}


Answers (1)

best_answer

Answer (4)

Applying energy conservation

\frac{1}{2}mv^{2}+\left [ -\frac{GMm}{R} \right ]=-\frac{GMm}{r}

\Rightarrow \frac{1}{2}m.K^{2}.\frac{2GM}{R}-\frac{GMm}{R}=-\frac{GMm}{r}\frac{R}{R}

\Rightarrow K^{2}-1=\frac{-R}{r}

\Rightarrow r=\frac{R}{1-K^{2}}

Posted by

rishi.raj

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