Question

What is connected motion?

Answer 1

$\mathfrak{\large {\underline {\underline{Answer \: : - }}}}$

Connected Motion :

Consider two masses m₁, and m₂ (< m₁) connected to the two ends of an inextensible string passing over a smooth frictionless pulley. Let a be the acceleration produced in the masses. While the heavier mass m, moves down with acceleration a, the lighter mass me moves up with acceleration a. Let T be the tension in the string.

$\huge \boxed{ \sf {a =\frac{m_1 - m _2}{m_1 +m _2}g}}$

$\huge \boxed{ \sf {T=\frac{2m_1 m _2}{m_1 +m _2}g}}$

Answer 2

When the motion of one body is directly connected to the motion of another body then these bodies are said to be under connected motion.

Motion of Two Bodies Connected by a String over a pulley on different planes.

Consider a light inextensible string passing over a smooth pulley, , so that the tension (T) in both the strings is same.  

Let mass m1 is greater than mass m2. Since the string is inextensible, the upward acceleration of mass m2 will be equal to the downward acceleration of mass m1. This acceleration is given by

and tension in the string,