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?

Answer:

                                                                                       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 \[a=\frac{F}{m}=\frac{10}{{{m}_{1}}+{{m}_{2}}}=\frac{10}{2+\frac{2}{3}}=\frac{30}{8}=3.75\,\text{m}{{\text{s}}^{-2}}\]