question_answer

Two masses \[{{m}_{1}}=5kg\] 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,                                                      \[{{m}_{1}}=5kg,\,{{m}_{2}}=4.8kg\],                 \[g=9.8m/{{s}^{2}}\] \[\therefore \]\[a=\left( \frac{5-4.8}{5+4.8} \right)\times 9.8\]                 \[=\frac{0.2}{9.8}\times 9.8=0.2m/{{s}^{2}}\]