The acceleration of object A is 1.023 x 10⁴ m/s².
The law states that two objects in the universe exert a force on each other which is proportional to the square of distance between them and product of mass of the two objects.
[tex]F = \frac{GmM}{R^2} [/tex]
Equate the force to Newton's second law of motion,
[tex]F = ma = \frac{GMm}{R^2} \\\\ a = \frac{GM}{R^2} [/tex]
The acceleration of object A is calculated as follows;
[tex]a = \frac{6.67 \times 10^{-11} \times 4.21 \times 10^{21}}{(5.24 \times 10^3)^2} \\\\ a = 1.023 \times 10^4 \ m/s^2[/tex]
Learn more about Newton's law of universal gravitation here: https://brainly.com/question/9373839