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# A force applied to an object of mass $\text{m1}$ produces an acceleration of 3.00 ms$^{-2}$. The same force applied to a second object of mass $\text{m2}$ produces an acceleration of 1.00 ms$^{-2}$. What is the value of the ratio $\large\frac{\text{m1}}{\text{m2}}$?

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• According to Newton's second law: When viewed from an inertial reference frame, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
According to Newton's second law, $F = ma$
$\Rightarrow F = m1a1 = m2a1$.
Given, $a1 = 3 m/s^2$ and $a2 = 1 m/s^2, \rightarrow F = m1 \times 3 = m2 \times 1 \rightarrow \large\frac{m1}{m2}$$= \large\frac{1}{3}$