Answer:
r = 50.47 x 10³ m = 50.47 km
Explanation:
Using the formula for the acceleration due to gravity:
[tex]g = \frac{Gm}{r^2}[/tex]
where,
g = acceleration due to gravity on the surface of asteroid = 0.0288 m/s²
G = Universal Gravitational Constant = 6.67 x 10⁻¹¹ Nm²/kg²
m= mass of asteroid = 1.1 x 10¹⁸ kg
r = radius of asteroid = ?
Therefore,
[tex]0.0288\ m/s^2 = \frac{(6.67\ x\ 10^{-11}\ Nm^2/kg^2)(1.1\ x\ 10^{18}\ kg)}{r^2} \\\\r = \sqrt{\frac{(6.67\ x\ 10^{-11}\ Nm^2/kg^2)(1.1\ x\ 10^{18}\ kg)}{0.0288\ m/s^2}}[/tex]
r = 50.47 x 10³ m = 50.47 km
