Question

The escape velocity of a body from the earth is 11.2 km/s. If the radius of a planet be half the radius of earth and its mass be one fourth that of earth. The escape velocity for the planet will be :

• A. 8 km/s
• B. 4 km/s
• C. 6 km/s
• D. 12 km/s

Answer 1

Answer: (A)

Escape velocity for earth is given by $ {{\upsilon }_{es(e)}}=\frac{\sqrt{2GMe}}{{{R}_{e}}} $ ?...(l) Escape velocity for planet is given by $ {{\upsilon }_{es(e)}}=\frac{\sqrt{2GMp}}{{{R}_{p}}} $ ...(ii) From equation (i) and (ii) we have $ \frac{{{\upsilon }_{es(p)}}}{{{\upsilon }_{es(e)}}}=\sqrt{\frac{{{M}_{p}}}{{{M}_{e}}}\times \frac{{{R}_{e}}}{{{R}_{p}}}} $ (Given, $ {{M}_{p}}=\frac{{{M}_{e}}}{4},{{R}_{p}}=\frac{{{R}_{e}}}{2} $ ) So, $ \frac{{{\upsilon }_{es(p)}}}{{{\upsilon }_{es(e)}}}=\sqrt{\frac{{{M}_{e}}}{4\times {{M}_{e}}}\times \frac{2\times {{R}_{e}}}{{{R}_{e}}}}=\frac{1}{\sqrt{2}} $ So, $ {{\upsilon }_{es(p)}}=\frac{{{\upsilon }_{e}}}{\sqrt{2}}=\frac{11.2}{\sqrt{2}}=7.92 $ $ =8km/s $