Question

In first case a mass M is split into two parts with one part being 1/6.334 th of the original mass. In second case M is split into two equal parts. In both the cases the two parts are separated by same distance. What ratio of the magnitude of the gravitational force in first case to the magnitude of the gravitational force in the second case

Answer 1

Answer:

$F_r=0.132:0.25$

Explanation:

From the question we are told that:

$M_1=M*\frac{1}{6.334}$

Therefore

$M_2=M-M*\frac_{1}{6.334}$

$M_2=M*\frac{5.334}{6.334}$

Generally the equation for Gravitational force of attraction is mathematically given by

For Unequal split

$F=\frac{GM_1M_2}{d^2}$

$F=\frac{G(M*\frac_{1}{6.334})(M*\frac{5.334}{6.334})}{d^2}$

$F=\frac{GM^2}{d^2}*(0.132)$

For equal split

$F=\frac{GM_1M_2}{d^2}$

$F=\frac{G(\frac{M}{2})((\frac{M}{2}}{d^2}$

$F=0.25 \frac{GM^2}{d^2}$

Therefore the ratio of the gravitational force is

$F_r=0.132:0.25$