Question

A force of 500 N acts on a body of mass x and gives it an acceleration of 200 m/s². The same force acting on another body of mass y gives it an acceleration of 40 m/s². If x and y are tied together and the same force as above, acts on them, what acceleration is produced in the combination?

Answer 1

We know,
Force=Mass x Acceleration
According to question,
$$\begin{gathered} 500=\mathrm{x}\times 200 \\ \mathrm{Mass}\mathrm{of}\mathrm{body},\mathrm{x}=\frac{500}{200}=2.5\mathrm{kg} \\ \mathrm{And} \\ 500=\mathrm{y}\times 40 \\ \mathrm{Mass}\mathrm{of}\mathrm{body},\mathrm{y}=\frac{500}{40}=12.5\mathrm{kg} \\ \mathrm{If}\mathrm{x}\mathrm{and}\mathrm{y}\mathrm{are}\mathrm{tied}\mathrm{together}, \\ \mathrm{Total}\mathrm{mass}=\mathrm{x}+\mathrm{y}=2.5+12.5=15\mathrm{kg} \\ \mathrm{Again}\mathrm{Force},\mathrm{F}=500\mathrm{N} \\ \mathrm{Then}, \\ 500=15\times \mathrm{a} \\ \mathrm{or}\mathrm{a}=\frac{500}{15}=33.3\mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$
This is the acceleration produced in the combination.