Question

a planet whose mass is twice of the Earth and the radius also twice of the earth will acceleration due to gravity
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Answer 1

Explanation:

mg = G Mm / r^2

=> g = GM / r^2

Planet mass = 2M

Radius of planet = 2r

then,

g' = 2GM / 4r^2 = GM / 2 r^2 = g / 2

So acceleration due to gravity on planet , g' = g/2

ANS.

Answer 2

Given:

The mass and radius of a planet are twice the mass and radius of the earth.

To Find:

Acceleration due to gravity on the planet.

Solution:

We know that acceleration due to gravity on the surface of an object is given by

          $g=G\frac{M}{r^2}$

where $G$ is the universal gravitational constant, $M$ is the mass of that object, and $r$ is the radius of the object.

Acceleration on the surface of the earth,

         $g_e=G\frac{M_e}{r_e^2}$

Acceleration on the surface of the planet,

        $g_p=G\frac{M_p}{r_p^2}$

   ⇒ $g_p=G\frac{2M_e}{(2r_e)^2}$

   ⇒ $g_p=\frac{1}{2} g_e$

Hence, acceleration due to gravity on the planet is equal to half of the acceleration due to gravity on earth.