A rocket has to be launched from earh in such a way that it never returns. If E is the minimum energy delivered by the rocket launcher what should be the minimum energy that the launcher should have if the same rocket has launcher from the surface of the moon ? Assume that the density of the earth and the moon are equal and that the earth's volume is `64` times the volume of the moon

Options

A. `E/64`
B. `E/32`
C. `E/16`
D. `E/4`

Answer

C

Explanation

`V_E=64V_m rArr R_E=4R_M " " g_E=G rho(4pi)/3 R_E rArr g_M/g_E=R_M/R_E rArr g_M=g_E/4`
`E prop v_e^2 rArr E prop gR " " E_M/E_E =g_M/g_E R_M/R_E rArr E_M/E = 1/4xx1/4 rArr E_M=E/16`