Question

The radius in kilometre, to which the present -ad ins of the earth (R =6400 km) is to be compressed, so that the escape velocity is increased to ten times, is:

• A. 6.4
• B. 64
• C. 640
• D. 4800

Answer 1

Answer: (B)

Escape velocity on earth is given by $v_{es}=\sqrt{\frac{2GM}{R}}$ $\frac{v_{e{s}_1}}{v_{e{s}_2}}=\sqrt{\frac{2GM}{R_1}\times \frac{R_2}{2GM}}$ (Given $v_{e{s}_2}=10v_{e{s}_1}$ ) $\frac{v_{e{s}_1}}{v_{e{s}_2}}=\sqrt{\frac{R_2}{R_1}}$ $\frac{{(v_{e{s}_1})}^2}{{(10v_{es})}^2}=\frac{R_2}{R_1}$ $\Rightarrow$ $\frac{1}{100}=\frac{R_2}{R_1}$ or $R_2=\frac{R_1}{100}=\frac{6400}{100}=64km$