Motion of connected bodies:

Analyze motion of connected bodies that is connected by pulleys.

Sol: The given figure shows a light and inextensible string passing over smooth and weightless pulley. Two bodies having weights W₁  and W₂  are attached to the two ends of string.

Let W₁>W₂, weight W₁ will move downwards, while smaller weight W₂ will move upwards. For the inextensible string, upward acceleration of weight W₂ will be equal to downward acceleration of weight W₁.

As string is light and inextensible and passing over the smooth pulley, the tension of string will

be same on both the sides of pulley.

Consider the Motion of weight W₁( down ward)

W₁-T = m₁.a                                                                                                                                     ...(i)

T-W₂ = m₂.a                                                                                                                                    ...(ii)

Solved both equation for finding value of Tension (T) or acceleration (a)