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?                          [AIEEE 2004]

\[(g=9.8\text{ }m/{{s}^{2}})\]

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 :

[a] 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, \[{{m}_{1}}=5kg,{{m}_{2}}=4.8kg,g=9.8m/{{s}^{2}}\]

\[\therefore \]      \[a=\left( \frac{5-4.8}{5+4.8} \right)\times 9.8\]

\[=\frac{0.2}{9.8}\times 9.8\]

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