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  • An asteroid is moving directly towards the centre of the earth. When at a distance of 10 R (R is the radius of the earth) from the earths centre , it has a speed of 12 km/s . Neglecting the effect of earths atmosphere, what will be the speed of the ast

An asteroid is moving directly towards the centre of the earth. When at a distance of 10 R (R is the radius of the earth) from the earths centre , it has a speed of 12 km/s . Neglecting the effect of earths atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is 11.2 km/s ) ? Give your answer to the nearest integer in kilometer/s _______ .
Option: 1 16
Option: 2 32
Option: 3 48
Option: 4 64
 

Answers (1)

best_answer

We will apply energy conservation here:-

 

\begin{array}{l}{\mathrm{KE}_{1}+\mathrm{PE}_{1}=\mathrm{KE}_{\mathrm{f}}+\mathrm{PE}_{\mathrm{f}}} \\ \\ {\frac{1}{2} \mathrm{mu}_{0}^{2}+\left(-\frac{\mathrm{GMm}}{10 \mathrm{R}}\right)=\frac{1}{2} \mathrm{mv}^{2}+\left(-\frac{\mathrm{GMm}}{\mathrm{R}}\right)} \\ \\{\mathrm{v}^{2}=\mathrm{u}_{0}^{2}+\frac{2 \mathrm{GM}}{\mathrm{R}}\left[1-\frac{1}{10}\right]} \\ \\ {\mathrm{v}=\sqrt{\mathrm{u}_{0}^{2}+\frac{9}{5} \frac{\mathrm{GM}}{\mathrm{R}}}} \\ \\ {=\sqrt{12^{2}+0.9(11.2)^{2}}} \\ \\ {=16.028 \mathrm{km} / \mathrm{s}} \\ {=16}km/s\end{array}

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vishal kumar

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