A smooth massless string passes over a smooth fixed pulley. Two masses m_(1) and m_(2) (m_(1) gt m_(2)) are tied at the two ends of the string. The masses are allowed to move under gravity starting from rest. The total external force acting on the two masses is

A smooth massless string passes over a smooth fixed pulley. Two masses

1.	A smooth massless string passes over a smooth fixed pulley. Two masses m_(1) and m_(2) (m_(1) gt m_(2)) are tied at the two ends of the string. The masses are allowed to move under gravity starting from rest. The total external force acting on the two masses is
Answer» `(m_(1) + m_(2))G` `((m_(1) - m_(2)))/(m_(1) + m_(2))g` `(m_(1) - m_(2))g` `((m_(1) + m_(2))^(2))/(m_(1) - m_(2))g` Solution :If a is the acceleration of the TWO masses and T is the tension in the two sides of the string, then `m_(1)g -T = m_(1) a"" `(1) ` T - m_(2)g = m_(2)a""`…(2) Now from equations (1) and (2), we get, a = `((m_(1) - m_(2)))/(m_(1) + m_(2))g ` Therefore, TOTAL external force ` = (m_(1) + m_(2)) a = (m_(1) - m_(2))g` The option C is correct.