Question

The radius of newly discovered planet is 3 times that of the earth but having same density. If acceleration due to gravity on surface of the earth is g and that on surface of new planet is g′, then​

Answer 1

Explanation:

If the mass and radius of the new planet be M

′

and R

′

,

then for same density as earth,

R

′

=3R & M

′

=27M [MαV, where VαR

3

]

Now for Earth,

g=

R

2

GM

→(1)

and for new planet,

g

′

=

R

′2

GM

′

=

(3R)

2

G(27M)

=3(

R

2

GM

)=3g.

solution

Answer 2

Given,

The radius of the newly discovered planet is 3 times the earth but has the same density.

If the acceleration due to gravity on the earth is 'g'.

To Find,

The acceleration is due to gravity on the surface of a new planet.

Solution,

We can solve this mathematical problem using a mathematical formula.

The acceleration due to gravity on the new planet can be found using the relation,

⇒ g = $\frac{GM}{R^{2} }$

but M = $\frac{4}{3} \pi R^{3} p$, where p is density.

∴  g = $\frac{G * \frac{4}{3} \pi R^{3} p }{R^{2} }$ = $G * \frac{4}{3}\pi R p$

⇒ g ∝ R

∴  $\frac{g'}{g} = \frac{R'}{R}$

⇒ $\frac{g'}{g} = \frac{3R}{R}$ = 3

∴  g' = 3g

Hence, the acceleration due to gravity on the surface of a new planet is 3 times that of earth.