The distance between two objects A and B is r | vedclass

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(A) According to the inverse square law,the gravitational force between $A$ and $B$ is given by:$F = G \frac{m_A m_B}{r^2}$The acceleration of object

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$a_A / r^2$

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(A) According to the inverse square law,the gravitational force between $A$ and $B$ is given by:$F = G \frac{m_A m_B}{r^2}$The acceleration of object $A$ is $a_A = \frac{F}{m_A} = \frac{G m_B}{r^2}$ ... $(1)$For the second case,where the force is inversely proportional to the fourth power of the distance:$F' = G \frac{m_A m_B}{r^4}$The new acceleration of object $A$ is $a_A' = \frac{F'}{m_A} = \frac{G m_B}{r^4}$Substituting the expression from equation $(1)$ into the new acceleration formula:$a_A' = \frac{1}{r^2} \left( \frac{G m_B}{r^2} \right) = \frac{a_A}{r^2}$Therefore,the acceleration of object $A$ becomes $\frac{a_A}{r^2}$.

The distance between two objects $A$ and $B$ is $r$. The gravitational force between them is inversely proportional to the square of the distance. If the gravitational force between these two objects were inversely proportional to the fourth power of the distance,find the acceleration of object $A$.

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