question_answer

    Two masses\[{{m}_{1}}=5\,kg\]and\[{{m}_{2}}=4.8\text{ }kg\] tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when lift is free to move? \[(g=9.8m/{{s}^{2}})\]

A)  \[0.2\text{ }m/{{s}^{2}}\]                           

B)  \[9.8\text{ }m/{{s}^{2}}\]                  

C)  \[5\text{ }m/{{s}^{2}}\]                               

D)  \[4.8\text{ }m/{{s}^{2}}\]                  

Correct Answer: A

Solution :

                 On releasing, the motion of the system will be according to figure. \[{{m}_{1}}g-T={{m}_{1}}a\]                                       ...(i) and        \[T-{{m}_{2}}g={{m}_{2}}a\]                                       ?(ii) On solving; \[a=\left( \frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right)g\]                       ?.(iii) Here, \[{{m}_{1}}=5kg,{{m}_{2}}=4.8\,kg,\]                 \[g=9.8\,m/{{s}^{2}}\] \[\therefore \]  \[a=\left( \frac{5-4.8}{5+4.8} \right)\times 9.8\]                 \[=\frac{0.2}{9.8}\times 9.8=0.2\,m/{{s}^{2}}\]