• # question_answer                                       Force of 10 N applied to a mass ${{m}_{1}}$ produces an acceleration of 5 $\text{m}{{\text{s}}^{\text{-2}}}$ and when applied to mass ${{m}_{2}}$, produces an acceleration of 15 $\text{m}{{\text{s}}^{\text{-2}}}$in the mass. How much acceleration will the same force produce if the two masses are tied together?

We know that, F = ma $10={{m}_{1}}\times 5$ or            ${{m}_{1}}=\frac{10}{5}=2kg$ Also, ${{m}_{2}}=\frac{10}{15}=\frac{2}{3}kg$                                  Required acceleration produced when the masses are tied together $a=\frac{F}{m}=\frac{10}{{{m}_{1}}+{{m}_{2}}}=\frac{10}{2+\frac{2}{3}}=\frac{30}{8}=3.75\,\text{m}{{\text{s}}^{-2}}$