Question

The escape velocity of an atmospheric particle which is 1000 km above the earth's surface, is (radius of the earth is 6400 km and g=9.8 $m/s^2$)

• A. $6.5km/S$
• B. $8km/S$
• C. $10.4km/S$
• D. $11.2km/S$

Answer 1

The correct option is C $10.4km/S$

$V_e=\sqrt{\frac{2GM}{R+h}}$

$V_e=\sqrt{\frac{2GM}{R}}$

$\frac{V_e}{V_e^{\prime }}=\frac{\sqrt{R+h}}{\sqrt{R}}$

$=\sqrt{\frac{6400+1000}{6400}}=\frac{7400}{6400}=\sqrt{1.15}=1.072$

$v^{\prime }=\frac{11.2}{1.067}=\frac{11.2}{115}=\frac{10}{10}$

$9.73=10.46$km/s

$=10\times {10}^3$m/s

$V^1={10}^4$ m/s.