Question

Please help me please help​

Answer 1

Answer:

Answer → Distance is 5 × 10⁴ km

Explanation:

Gravitational formular

${ \tt{F = \frac{GMm}{ {r}^{2} } }}$

• F is the gravitational force
• G is the universal gravitational constant
• r is the separation distance
• M & m are the masses

For the first case;

${ \tt{F _{1} = \frac{GMm}{2.5 \times {10}^{4} } }}$

For the second case;

${ \tt{F _{2} = \frac{GMm}{r _{2}} }}$

but F2 = ½F1

Therefore, F1 = 2F2

Hence:

${ \tt{ \frac{GMm}{2.5 \times {10}^{4} } =2 \times \frac{GMm}{r _{2} } }} \\ \\ { \tt{ \frac{1}{2.5 \times {10}^{4} } = \frac{2}{r _{2} } }} \\ \\ { \tt{r _{2} = 2 \times 2.5 \times {10}^{4} }} \\ \\ { \underline{ \tt{ \: \: r _{2} = 5 \times {10}^{4} \: km \: \: }}}$