Two masses m₁ and m₂ exert a gravitational force of 12 N when they are 6m apart, if they are now 3 m apart, the gravitational force is 48.02 N.
The gravitational force is given by:
[tex] F = \frac{Gm_{1}m_{2}}{d^{2}} [/tex]
Where:
m₁ and m₂ are the masses of the first and second body, respectively
G: is the gravitational constant = 6.67x10⁻¹¹ N*m²*kg⁻²
d: is the distance between m₁ and m₂
When the two masses exert a gravitational force of 12 N when they are 6 m apart, we have:
[tex] F_{1} = \frac{Gm_{1}m_{2}}{d_{1}^{2}} [/tex]
[tex] 12 N = \frac{6.67 \cdot 10^{-11} N*m^{2}kg^{-2}*m_{1}m_{2}}{(6 m)^{2}} [/tex]
[tex] m_{1}m_{2} = \frac{12 N*(6 m)^{2}}{6.67 \cdot 10^{-11} N*m^{2}kg^{-2}} = 6.48 \cdot 10^{12} \:kg^{2} [/tex]
When the distance is 3 meters, the gravitational force is:
[tex] F_{2} = \frac{Gm_{1}m_{2}}{d_{2}^{2}} = \frac{6.67 \cdot 10^{-11} N*m^{2}kg^{-2}*6.48 \cdot 10^{12} \:kg^{2}}{(3 m)^{2}} = 48.02 N [/tex]
Therefore, the gravitational force will be 48.02 N if the masses are 3 m apart.
Learn more about gravitational force here:
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- https://brainly.com/question/807785?referrer=searchResults
I hope it helps you!
