A block A of mass m₁ rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of table and from its other end another block B of mass m₂ is suspended. The coefficient of kinetic friction between the block and the table is µ_k . When the block A is sliding on the table, the tension in the string is :-

\(\frac{m_1m_2(1 + \mu_k )g}{m_1 + m_2}\)

For the motion of both blocks : 

\(m_2 g - T = m_2 a\)

\(T - \mu_k m_1g = m_1 a\)

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

For the motion of block of mass m₂

\(m_2 g - T = m_2 [\frac{m_2 - \mu_k m_1}{m_1 + m_2}]g

⇒ T = \(\frac{m_1m_2(1 + \mu_k )g}{m_1 + m_2}\)