Fig, shows a light and inextensible string passing over a smooth and weightless pulley. Two bodies of weights W1 and W2 are attached to the two ends of the string.
Let W1>W2, the weight W1 will move downwards, whereas smaller weight W2 will move upwards. For an inextensible string, the upward acceleration of the weight W2 will be equal to the downward acceleration of the weight W1.
As the string is light and inextensible and passing over a smooth pulley, the tension of the string will be same on both sides of the pulley. Consider the Motion of weight W1(Down motion) W1-T = m1.a ...(i)
Consider the Motion of weight W2 (up motion)
T-W2 = m2.a ...(ii)
Solved both the equation for finding the value of Tension (T) or acceleration (a)