If density of a planet is double that of the earth and the radius 1.5 times that of the earth

If density of a planet is double that of the earth and the radius 1.5 times that of the earth , the acceleration due to gravity on the surface of the planet is:

• A

  $$\dfrac{3}{4}$$ times that on the surface of the earth

• B

  3 times that on the surface of the earth

• C

  $$\dfrac{4}{3}$$ times that on the surface of the earth

• D

  6 times that on the surface of the earth

The correct option is B

We have,

The density of the planet is double of the earth

So, $$D_p=2D_e$$

The radius of  the planet is equal to 1.5 times the radius of the earth

So, $$R_p=1.5R_e$$

Since$$ D_p=2D_e$$

$$\dfrac{M_p}{\dfrac{4}{3}\pi R_p^3}=2\times\dfrac{M_e}{\dfrac{4}{3}4R_e^3}$$

$$M_p=2\times(1.5)^3M_e$$

So,

$$\dfrac{g_p}{g_e}=\dfrac{\dfrac{GM_p}{R_P^2}}{\dfrac{GM_e}{R_e}^2}$$

$$g_P=3g_e$$