Given mass of the moon is (1/81) of the mass of the earth and corresponding radius is (1/4) of the earth. If escape velocity on the earth surface is 11.2 km/s, the value of same on the surface of the moon is

Question

Given mass of the moon is (1/81) of the mass of the earth and corresponding radius is (1/4) of the earth. If escape velocity on the earth surface is 11.2 km/s, the value of same on the surface of the moon is (A) 0.14 km/s (B) 0.5 km/s (C) 2.5 km/s (D) 5 km/s

Tardigrade Admin · Accepted Answer

On earth ve=√(2GM/R) =11.2 km/s On moon vm=√(2GM× 4/81× R) =(2/9)√(2GM/R) =(2/9)× 11.2=2.5 km/s

Q. Given mass of the moon is $\frac{1}{81}$ of the mass of the earth and corresponding radius is $\frac{1}{4}$ of the earth. If escape velocity on the earth surface is 11.2 km/s, the value of same on the surface of the moon is

0.14 km/s

0.5 km/s

2.5 km/s

5 km/s

On earth $v_{e} = \frac{2 GM}{R}$ $= 11.2 km / s$ On moon $v_{m} = \frac{2 GM \times 4}{81 \times R}$ $= \frac{2}{9} \frac{2 GM}{R}$ $= \frac{2}{9} \times 11.2 = 2.5 km / s$

Q. Given mass of the moon is 811​ of the mass of the earth and corresponding radius is 41​ of the earth. If escape velocity on the earth surface is 11.2 km/s, the value of same on the surface of the moon is