Q. The distance between the earth and the moon is $3.85 \times 10^{8}$m. At what distance from the earth’s centre, the intensity of gravitational field will be zero? The masses of earth and moon are $5.98 \times 10^{24}\ kg\ and\ 7.35 \times 10^{22}\ kg$ respectively
A) $3.47 \times 10^{8}m$
B) $0.39 \times 10^{8}m$
C) $1.82 \times 10^{8}m$
D) None of these
Explanation
(a) $\frac{GM_{e}}{x^{2}} = \frac{GM_{m}}{(r - x)^{2}}$
or $\frac{r - x}{x} = \sqrt{\frac{M_{m}}{M_{e}}} = \sqrt{\frac{7.35 \times 10^{22}}{5.98 \times 10^{24}}}$
or $r = 0.11x + x = 1.11x$
$x = r/1.11 = 3.85 \times 10^{8}/1.11$
$= 3.47 \times 10^{8}\ m$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.