MCQ
Escape velocity of an atmospheric particle which is $1000 \,km$ above the earth's surface, is ..........$km / s$ (radius of earth is $6400 \,km$ and $g=9.8 \,m / s ^2$ )
- A$6.5$
- B$8$
- ✓$10.4$
- D$11.2$
✓
Answer
Correct option: C.
$10.4$
c
(c)
(c)
$V _e=\sqrt{\frac{2 GM }{ R + h }}$
$V _{ e }=\sqrt{\frac{2 GM }{ R }}$
$\frac{ V _e}{ V _e^{\prime}}=\frac{\sqrt{ R + h }}{\sqrt{ R }}$
$=\sqrt{\frac{6400+1000}{6400}}=\frac{7400}{6400}=\sqrt{1.15}=1.072$
$V ^{\prime}=\frac{11.2}{1.067}=\frac{11.2}{115}=\frac{10}{10}$
$9.73=10.46\,km / s$
$=10 \times 10^3\,m / s$
$V ^1=10^4\,m / s$
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