Question

Find the radius of planet where g is
2 times the g of earth, while its mass doesn't
change​

Answer 1

Answer:

$\boxed{\mathfrak{R_p = \frac{R_e}{ \sqrt{2} } }}$

Explanation:

Acceleration due to gravity of Earth = $\rm g_e$

Acceleration due to gravity of Planet = $\rm g_p$

Radius of Earth = $\rm R_e$

Radius of Planet = $\rm R_p$

Acceleration due to gravity is given as:

$\boxed{ \bold{g = \frac{GM}{R^2}}}$

As mass of Earth and the planet is same. So,

$\rm \bold{g \propto \dfrac{1}{R^2}}$

According to question;

$\rm \implies g_p = 2g_e \\ \\ \rm \implies \frac{1}{ {R_p}^{2} } = 2 \times \frac{1}{ {R_e}^{2} } \\ \\ \rm \implies \frac{1}{R_p} = \sqrt{ \dfrac{2}{ {R_e}^{2} } } \\ \\ \rm \implies R_p = \sqrt{ \dfrac{ {R_e}^{2} }{2} } \\ \\ \rm \implies R_p = \frac{R_e}{ \sqrt{2} }$

$\therefore$

$\rm Radius \ of \ Planet \ (R_p) = \dfrac{Radius \ of \ earth \ (R_e)}{ \sqrt{2} }$