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 \[{{m}_{1}}g-T={{m}_{1}}a\] \[T-{{m}_{2}}g={{m}_{2}}a\] \[a=\left( \frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right)g\] \[a=\left( \frac{5-48}{5+4.8} \right)\times 9.8\] \[=\frac{0.2}{9.8}\times 9.8=0.2\,m/{{s}^{2}}\]