question_answer

Two masses\[{{m}_{1}}=5\text{ }kg\]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?

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

B)  \[9.8m/{{s}^{2}}\]

C)  \[5m/{{s}^{2}}\]            

D)  \[4.8\text{ }m/{{s}^{2}}\]

Correct Answer: A

Solution :

                On releasing the motion of the system will be according to figure                 \[{{m}_{1}}g-T={{m}_{1}}a\]                 \[T-{{m}_{2}}g={{m}_{2}}a\]                 \[a=\left( \frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right)g\]                 \[a=\left( \frac{5-48}{5+4.8} \right)\times 9.8\]                 \[=\frac{0.2}{9.8}\times 9.8=0.2\,m/{{s}^{2}}\]