question_answer

Two bodies have masses in the ratio 3:4. When a force is applied on first body, it moves with an acceleration of\[\text{6 m}/{{\text{s}}^{\text{2}}}\]. How much acceleration will the same force produce in the other body?

Answer:

\[{{m}_{1}}:{{m}_{2}}=3:4;\] \[{{a}_{1}}=6m/{{s}^{2}}\] But, \[a\propto \frac{1}{m}\] (Since F is same) \[\Rightarrow ma=cons\tan t.\] \[\Rightarrow \,{{m}_{1}}{{a}_{1}}={{m}_{2}}{{a}_{2}}=cons\tan t\] \[\Rightarrow \frac{{{m}_{1}}}{{{m}_{2}}}=\frac{{{a}_{2}}}{{{a}_{1}}}\Rightarrow \frac{3}{4}=\frac{{{a}_{2}}}{6}\] \[\Rightarrow 4{{a}_{2}}=18m/{{s}^{2}}\Rightarrow {{a}_{2}}=\frac{18}{4}m/{{s}^{2}}\] \[\Rightarrow {{a}_{2}}=4.5\,\,m/{{s}^{2}}\]