Question

The mass of a planet is 1/10th that of earth and its diameter is half that of earth. The acceleration due to gravity at the planet will be

Answer 1

Hi there!
Here's the answer:

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¶ SOLUTION :

Given,

Mass of planet = $\frac{1}{10}$(Mass of Earth)

Diameter of planet = $\frac{1}{2}$(Diameter of Earth)

$\implies$Radius of planet =$\frac{1}{4}$(Radius of Earth)

Let R be Radius of the Earth
and M be Mass of the Earth

So
Mass of planet =$\frac{M}{10}$

Radius of planet =$\frac{R}{4}$

We have,
Acceleration due to gravity on Earth$g = \frac{GM}{R^{2}}$

Let g' be acceleration due to gravity on planet

$g' = \frac{G(\frac{M}{10})}{(\frac{R}{4})^{2}}$

$\implies g' = \frac{GM}{R^{2}}×\frac{16}{10} = 1.6g$

Therefore,
The acceleration due to gravity on planet is 1.6 times the acceleration due to gravity on Earth.

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