A system consists of three masses m1, m2 and m3 connected by a string passing over a pulley P. The mass m1 hangs freely and m2 and m3 are on a rough horizontal table (the coefficient of friction = µ). The pulley is frictionless and of negligible mass. The downward acceleration of mass m1 is (Assume m1 = m2 = m3 = m)
Answer & explanation
Correct answer: option 3
\( m_1g - T_1 = m_1a \) ---------(1)
\( T_1 - f_1 - T_2 = m_2a \) ------------(2)
\( T_3 - f_1 = m_3a \) -----------(3)
On solving above equation we get
m1 = m2 = m3 = m
mg - 2μmg = 3ma
⇒ a = \(\frac{g(1-2\mu)}{3}\)