Question

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

Answer 1

Explanation:

The acceleration due to gravity on the surface is given as

r

2

Gm

If the mass and the radius are doubled then the acceleration due to gravity will become

4r

2

G2m

Hence the acceleration becomes one half.

Answer 2

Let, planet is the Earth.

${ \bf{ \underline{ \red{ \underline{Given \: data:-}}}}}$

• Mass of earth is doubled
• Radius of earth is tripled

${ \bf{ \underline{ \red{ \underline{Solution:-}}}}}$

To find acceleration due to gravity ( g )

Here, M : mass of the Earth, R : radius of the Earth, G : gravitational constant.

{Accirding to given}

${ \huge{ \bf{ \dashrightarrow{ \red{g \: = \frac{GM}{ {R}^{2} } }}}}}$

Now, according to given

${ \huge{ \bf{ \dashrightarrow{ \red{g \: = \frac{G(2M)}{ {3(R)}^{2} } }}}}}$

${ \huge{ \bf{ \dashrightarrow{ \red{g \: = \frac{2}{3} \frac{GM}{ {R}^{2} } }}}}}$

We know that R, M, and G are constant hence, g is depend on 2/3.

Hence, acceleration due to gravity is

${{ \bf{{ \red{g \: \: { { = }} \: { {\frac{2}{3}}} \frac{GM}{ {R}^{2} } }}}}}$