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The ratio of asteroid-A’s acceleration to asteroid-B’s acceleration is 37:7800.

Explanation:

Mass of asteroid-A = m = $7.80\times 10^{20} kg$

Mass of asteroid-B = m' = $3.70\times 10^{18} kg$

As we know , Force = mass × Acceleration

1) Force on an asteroid-A

$F = m\times a$

where , a is the acceleration due to force applied on asteroid-A

2) Force on an asteroid-B

$F' = m'\times a'$

where , a' is the acceleration due to the force applied on asteroid-B

Same force is exerted on the both the asteroids say F.

F = F'

$m\times a=m'\times a'$

$\frac{a}{a'}=\frac{3.70\times 10^{18} kg}{7.80\times 10^{20} kg}=\frac{37}{7800}$

The ratio of asteroid-A’s acceleration to asteroid-B’s acceleration is 37:7800.

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