Question

calculate the acceleration due to gravity on a celestial body whose mass is two times the earth and radius is half that of earth​

Answer 1

Answer:

The acceleration due to gravity of the celestial body = $\sqrt{8} * 9.8 = 27.718m/s^{2}$

Explanation:

The acceleration due to gravity due to any body having a  mass is, g is  $g = \sqrt{\frac{GM}{R^{2} } }$ ,

where G is the universal gravitational constant , M is the mass of the body, and R, the radius of the body.

We know, the acceleration due to gravity of  earth = g =  \sqrt{\frac{GM}{R^{2} } }    = 9.8m/s^2.

Given M , the mass( of celestial body) = 2M( of Earth)

and R( of celestial body) = (1/2)R( of Earth)

so the equation becomes,

$g = \sqrt{\frac{G * 2M}{\frac{R^{2} }{2^{2} } } } = \sqrt{8}* \sqrt{\frac{GM}{R^{2} } }$, ie the acceleration due to gravity of  the celestial body is sqrt 8 times that of Earth.