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  • A projectile is fired upwards from the surface of the earth with a velocity kve where is the esca

A projectile is fired upwards from the surface of the earth with a velocity kve where \mathrm{V_e} is the escape velocity and \mathrm{k<1. } If \mathrm{r} is the maximum distance from the centre of the earth to which it rises and \mathrm{R} is the radius of the earth, then \mathrm{r} is
 

Option: 1

\frac{\mathrm{R}}{\mathrm{k}^2}

 


Option: 2

\mathrm{\frac{2 \mathrm{R}}{1-\mathrm{k}^2}}
 


Option: 3

\mathrm{\frac{2 \mathrm{R}}{\mathrm{k}^2}}
 


Option: 4

\mathrm{\frac{\mathrm{R}}{1-\mathrm{k}^2}}


Answers (1)

best_answer

\mathrm{\left(\begin{array}{c} \text { Total } \\ \text { Mechanical } \\ \text { Energy } \end{array}\right)_{\text {surface }}=\left(\begin{array}{c} \text { Total } \\ \text { Mechanical } \\ \text { Energy } \end{array}\right)_{\mathrm{r}} }

\mathrm{ \Rightarrow-\frac{\mathrm{GMm}}{\mathrm{R}}+\frac{1}{2} \mathrm{~m}\left(\mathrm{kv}_{\mathrm{e}}\right)^2=-\frac{\mathrm{GMm}}{\mathrm{r}}+0 }

\mathrm{ \text { where } \mathrm{v}_{\mathrm{e}}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}} }

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

Hence option 4 is correct.


 

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