MOTION OF BODIES CONNECTED BY STRING PASSING OVER A SMOOTH PULLEY
Case-I: AT WOODS MACHINE:
Let two bodies of masses m1 and m2 respectively are connected by a light inextensible string passing over a massless smooth pulley. If m1>m2 , then mass m1 moves downwards and mass m2 moves upwards.
Equation of motion
For body A,\(
m_1 g - T = m_1 a
\) ,For body B, \(
T - m_2 g = m_2 a
\)
Solving, we get \(
a = \frac{{m_1 - m_2 }}
{{m_1 + m_2 }}g
\) ; and \(
T = \frac{{2m_1 m_2 }}
{{m_1 + m_2 }}g
\)
The reaction at the pulley \(
R = 2T = \frac{{4m_1 m_2 }}
{{m_1 + m_2 }}g
\)