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Question

Two bodies have a mass ratio of 3:4. The force applied on the bigger mass produces an acceleration of $12{\text{ms}}^{-2}$. What could be the acceleration of the other body, if the same force acts on it?

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Solution

Let the two masses be $m_1$ and $m_2$. We are given the mass ratio: $m_1:m_2=3:4$.

The larger mass is $m_2$, and its acceleration is $a_2=12{\text{ms}}^{-2}$. The force ($F$) applied to both bodies is the same.

According to Newton's Second Law, Force = Mass × Acceleration ($F=ma$). Since the force is the same for both bodies:

$$F=m_1{a}_1=m_2{a}_2$$

From the equality, we can set up a ratio:

$$\frac{m_1}{m_2}=\frac{a_2}{a_1}$$

We know the mass ratio $\frac{m_1}{m_2}$ is $\frac{3}{4}$.

$$\frac{3}{4}=\frac{12}{a_1}$$

Now, we solve for $a_1$:

$$a_1=\frac{4}{3}\times 12$$

The acceleration of the other body is:

$$a_1=16{\text{ms}}^{-2}$$

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