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(A) The acceleration due to gravity on the surface of a planet is given by $g = \frac{GM}{R^2}$.Let $M$ and $R$ be the mass and radius of the Earth,re

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$\frac{5}{8}$ times that on the surface of earth

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(A) The acceleration due to gravity on the surface of a planet is given by $g = \frac{GM}{R^2}$.Let $M$ and $R$ be the mass and radius of the Earth,respectively.For the given planet,the mass $M' = M - 0.10M = 0.9M = \frac{9}{10}M$.The radius $R' = R + 0.20R = 1.2R = \frac{12}{10}R = \frac{6}{5}R$.The acceleration due to gravity on the planet is $g' = \frac{GM'}{(R')^2}$.Substituting the values: $g' = \frac{G(\frac{9}{10}M)}{(\frac{6}{5}R)^2}$.$g' = \frac{G \cdot \frac{9}{10}M}{\frac{36}{25}R^2} = \frac{9}{10} \cdot \frac{25}{36} \cdot \frac{GM}{R^2}$.$g' = \frac{1}{2} \cdot \frac{5}{4} \cdot g = \frac{5}{8}g$.Thus,the acceleration due to gravity on the planet is $\frac{5}{8}$ times that on the surface of the earth.

If the mass of the planet is $10\%$ less than that of the earth and the radius is $20\%$ greater than that of the earth,the acceleration due to gravity on the planet will be

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