The given system of two masses and a pulley can be represented as shown in the following figure:Smaller mass, \\\\(m_1 = 8\\\\) kgLarger mass,\\\\( m_2 = 12 \\\\)kgTension in the string\\\\( = T\\\\)Mass \\\\(m_2\\\\), owing to its weight, moves downward with acceleration, and mass \\\\(m_1\\\\) moves upward.Applying Newton’s second law of motion to the system of each mass:For mass \\\\(m_1\\\\):The equation of motion can be written as:\\\\(T – m_1g = ma \\\\)… (i)For mass m2:The equation of motion can be written as:\\\\(m_2g – T = m2a\\\\) … (ii)Adding equations (i) and (ii), we get:\\\\((m2 - m1)g = (m1 + m2)a\\\\) \\\\(a = \\dfrac{(m2 - m1) g}{(m1 + m2) }\\\\) ....(iii)\\\\(=\\dfrac{ (12 - 8)}{ (12 + 8)} × 10 = \\dfrac{ 4 × 10}{ 20} = 2 ms-2\\\\)Therefore, the acceleration of the masses is 2 m/s2.Substituting the value of a in equation (ii), we get:\\\\(m_2g - T = m_2\\dfrac{(m_2 - m_1)g }{ (m_1 + m_2)}\\\\)\\\\(T = (m2 - \\dfrac{(m_2^2 - m1m2)}{(m1 + m2) }g\\\\) \\\\(= \\dfrac{2m_1m_2g }{(m_1 + m_2)}\\\\)\\\\(T= 2 × 12 × 8 × 10 / (12 + 8)\\\\)\\\\(T= 96 N\\\\)Therefore, the tension in the string is 96 N.