question_answer

The distance between two bodies A and B is r. Taking the gravitational force according to the law of inverse square of r, the acceleration of the body is a. If the gravitational force follows an inverse fourth power law, then what would be the acceleration of the body A?

Answer:

                For inverse square law, \[F=\frac{G{{m}_{1}}{{m}_{2}}}{{{r}^{2}}}\] \[\therefore \]  Acceleration of body \[A=\frac{F}{{{m}_{1}}}=\frac{G{{m}_{2}}}{{{r}^{2}}}=a\] For inverse fourth power law, \[F'=\frac{G{{m}_{1}}{{m}_{2}}}{{{r}^{4}}}\] Acceleration of body \[A=\frac{F'}{{{m}_{1}}}=\frac{G{{m}_{2}}}{{{r}^{4}}}=\frac{a}{{{r}^{2}}}\].