If the mass of the Sun were ten times smaller | vedclass

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(C) The acceleration due to gravity on the surface of the Earth is given by $g = \frac{GM}{R^2}$,where $M$ is the mass of the Earth and $R$ is the rad

Vedclass · Accepted Answer

$g$ on the Earth will not change.

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(C) The acceleration due to gravity on the surface of the Earth is given by $g = \frac{GM}{R^2}$,where $M$ is the mass of the Earth and $R$ is the radius of the Earth.Note that the mass of the Sun does not affect the value of $g$ on the Earth's surface.If the universal gravitational constant $G$ becomes $10G$,then the new acceleration due to gravity $g'$ becomes $g' = \frac{(10G)M}{R^2} = 10g$.Since $g' = 10g$,the acceleration due to gravity increases significantly.$1$. Raindrops will fall faster because the acceleration due to gravity is higher.$2$. Walking on the ground becomes more difficult because the effective weight of a person increases.$3$. The time period of a simple pendulum is $T = 2\pi \sqrt{\frac{l}{g}}$. Since $g$ increases,$T$ will decrease.$4$. The statement '$g$ on the Earth will not change' is incorrect because $g$ increases by a factor of $10$.

If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude,which of the following is not correct?

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