question_answer

Two masses\[{{m}_{1}}=5\,kg\]and\[{{m}_{2}}=4.8\,kg\]lied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when lift is free to move? \[(g=9.8\text{ }m/{{s}^{2}})\]   AIEEE  Solved  Paper-2004

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

B)        \[98\text{ }m/{{s}^{2}}\text{ }{{L}^{-1}}\]            

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