Given,

• mass of object A \( \rm (m_{A}) \) = 2500 kg
• mass of object B \( \rm (m_{B}) \) = 4000 kg
• distance between centers of two objects (d) = 600 m

Calculation of gravitational force between objects A and B

Let the gravitational force between objects A and B be \( \rm F_{G} \). We get,

\( \rm F_{G} = G \cdot \frac{m_{A} m_{B}}{d^{2}} \)

\( \rm = 6.67 \cdot 10^{-11} \cdot\frac{ 2500 \cdot 4000 }{ 600^{2} } \)

\( \rm = 1.85 \cdot 10^{-11} N\)

Hence, the required gravitational force between objects A and B is \( \rm = 1.85 \cdot 10^{-11} N\).

Calculation of height from the surface of the earth

The formula for the acceleration due to gravity at a place is \( \rm g = \frac{GM}{R^{2}} \).

Given,

• \( \rm g = 9.8 ms^{-2} \)
• \( \rm g' = 4 ms^{-2} \)

Using formula,

\( \rm g = \frac{GM}{R^{2}} \)

\( \rm g' = \frac{GM}{R'^{2}} \)

Dividing the above two equations, we get,

\( \rm \frac{g}{g'} = \frac{R'^{2}}{R^{2}} \)

\( \rm \frac{9.8}{4} = \left ( \frac{R'}{R} \right )^{2} \)

\( \rm \frac{R'}{R} = \sqrt{2.45} \)

\( \rm R' = 1.57 R \)

\( \rm R + h = 1.57 R \)

\( \rm h = 1.57 R - R \)

\( \rm h = 0.57 R \)

Hence, the object should be taken at a height 0.57 R above the surface of the earth so that the acceleration due to gravity becomes 4.0 \( \rm ms^{-2} \).