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Q38.

Expert-verifiedFound in: Page 134

Book edition
7th

Author(s)
Douglas C. Giancoli

Pages
978 pages

ISBN
978-0321625922

**If you doubled the mass and tripled the radius of a planet, by what factor would g at its surface change? **

The factor by which the acceleration due to gravity changes is $\frac{2}{9}$.

The increased mass of the planet is $m\text{'}=2m$.

The increased radius of the planet is $r\text{'}=3r$.

**The acceleration due to gravity of the planet does get affected by the variation in the mass and radius of the planet. As the mass doubles, the acceleration due to gravity will increase by a factor of 2.**

The relation of acceleration due to gravity is given by,

$g=G\frac{m}{{r}^{2}}$

Here, *G* is the gravitational constant, *m* is the mass and $r$ is the radius of the planet.

When the values of mass and radius are increased, the relation of acceleration due to gravity will become,

$\begin{array}{l}g\text{'}=G\frac{m\text{'}}{r{\text{'}}^{2}}\\ g\text{'}=G\frac{2m}{{\left(3r\right)}^{2}}\\ g\text{'}=G\frac{2m}{9{r}^{2}}\\ g\text{'}=\frac{2}{9}\left(g\right)\end{array}$

Thus, $\frac{2}{9}$ is the factor by which the acceleration due to gravity changes.

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