Let's call a the acceleration of the system. The problem says that the block m3 is static, so the acceleration is zero: a=0.
Calling [tex]T_1[/tex] the tension of the string between m1 and m3, and [tex]T_2[/tex] the tension of the string between m2 and m3, the problem can be solved by writing the following system of equations:
[tex]m_1 g-T_1=m1_a[/tex]
[tex]T_1-T_2=m_3 a[/tex]
[tex]T_2-m_2g=m_2a[/tex]
However, we know that a=0 and the problem asks only for [tex]T_1[/tex], so we just need to solve the first equation:
[tex]m_1 g -T_1 =0[/tex]
and so
[tex]T_1=m_1g=0.038~kg \cdot 9.81~m/s^2 = 0.37~N[/tex]
