Question

Two masses $m_1=5$ kg and $m_2=4.8$ kg tied to a string are hanging over a light
frictionless pulley. What is the acceleration of the masses when they are free to move? $(g=9.8m/s^2)$

• A. $0.2m/s^2$
• B. $9.8m/s^2$
• C. $5m/s^2$
• D. $4.8m/s^2$

Answer 1

The correct option is A $0.2m/s^2$

As there is no friction only gravitational forces are there.

hence gravitational force acting on $m_1$ is and on $m_2$ is $F_2=m_{2}g$

Now considering pulley as the isolated system and observing the forces acting on it are

$F_1=m_{1}g$ and

$F_2=m_{2}g$

hence the resultant force F

$F=(m_1+m_2)a=F_1-F_2$ as both $m_1$ and $m_2$ are both part of the system

$(m_1+m_2)a=m_{1}g-m_{2}g$

$a=\frac{m_1-m_2}{m_1+m_2}g=\frac{5-4.8}{5+4.8}\times 9.8=0.2$ $m/s^2$