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, ${\upsilon }_{es(p)}=\frac{{\upsilon }_e}{\sqrt{2}}=\frac{11.2}{\sqrt{2}}=7.92$ $=8km/s$