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

Options

A. 6.4
B. 64
C. 640
D. 4800

Answer

B

Explanation

Escape velocity , `v_e = sqrt((2GM)/(R )) i.e., v_e prop (1)/(sqrt R)`
Where M and R are the mass and the radius of the earth.
`therefore (v_(e_1))/(v_(e_2)) = sqrt(R_2/R_1) " or " 1/10 = sqrt(R_2/R_1) " or " 1/100 = R_2/R_1`
`R_2 = (R_1)/(100) = 6400/100 = 64km`