Question

Two masses m1 and m2 are attached to a string which passes over a frictionless smooth pulley.when m1 =10kg m2=6kg the accleration of masses is

Answer 1

you can draw FBDs for m1 and m2 for more clear understanding

Answer 2

Let acceleration of system of masses is a.
here $m_1$ is greater than $m_2$ then, acceleration of mass $m_1$ in downward and acceleration of mass $m_2$ in upward.

for mass $m_1$,
$m_1g-T=m_1a$.......(1)

for mass $m_2$,
$T-m_2g=m_2a$........(2)
here T is tension on string.

solve equations (1) and (2),

$m_1g-m_2g=m_1a+m_2a$

$a=\frac{(m_1-m_2)g}{(m_1+m_2)}$

now put values of $m_1,m_2$
so, $a=\frac{(10-6)10}{(10+6)}$
$a=2.5 m/s^2$