Suppose a planet exists whose mass and radius are half those of the earth. Calculate the acceleration due to gravity on the surface of this planet.

 We know $g=G\frac{M}{r^2}$

Here, $g\rightarrow$gravitational acceleration of the earth

$M\rightarrow$Mass

$r\rightarrow$radius of the earth

If the mass and radius of the planet are half of the earth.

Then, mass $=\frac{M}{2}$

Radius $=\frac{r}{2}$

Then, acceleration on the planet due to gravity $g'=G\frac{\frac{M}{2}}{(\frac{r}{2})^2}$

Or $g'=G\frac{\frac{M}{2}}{\frac{r^2}{4}}$

Or $g'=2\times G\frac{M}{r^2}$

Or $g'=2g$

Or $g'=2\times9.8\ m/s^2$   [value of $g$ on earth is $9.8\ m/s^2$]

Or $g'=19.6\ m/s^2$

Therefore, acceleration due to gravity on the surface of this planet is $19.6\ m/s^2$.

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Updated on: 10-Oct-2022

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