If the density of a small planet is the same | vedclass

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(A) The acceleration due to gravity $g$ on the surface of a planet is given by the formula $g = \frac{4}{3} \pi G R \rho$,where $G$ is the gravitation

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$0.2$

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(A) The acceleration due to gravity $g$ on the surface of a planet is given by the formula $g = \frac{4}{3} \pi G R \rho$,where $G$ is the gravitational constant,$R$ is the radius,and $\rho$ is the density.Since the density $\rho$ is the same for both the planet and the Earth,we have $g \propto R$.Let $g$ be the acceleration due to gravity on Earth and $g'$ be the acceleration due to gravity on the planet.Given that $R' = 0.2 R$,we can write the ratio as:$\frac{g'}{g} = \frac{R'}{R} = 0.2$.Therefore,$g' = 0.2 g$.

If the density of a small planet is the same as that of the Earth,while the radius of the planet is $0.2$ times that of the Earth,the gravitational acceleration on the surface of that planet is .......... $g$.

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