# Law of Motion V

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Fixed Pulley
It is a simple machine in the form of a circular disc or rim supported by spokes having groove at its periphery. It is free to rotate about an axis passing through its center and perpendicular to its plane.

Key Point
In case of light pulley, tension in the rope on both the sides of the pulley is same (to be proved in the rotational mechanics)
Anticlockwise Torque - Clockwise Torque = Moment of Inertia x Angular acceleration
Tx r - T2 x r = Iα
Since the pulley is light and hence considered to be massless, it’s moment of inertia

Different Cases of Fixed Pulley

i) Case - 1
Two bodies of different masses (m1 > m2) are attached at T1 two ends of a light string passing over a smooth light pulley
For vertical equilibrium of pulley
T1 = T + T = 2T
For vertical acceleration of mand m2
m1g - T = m1a and T - m2g = m2a
maccelerates downwards and maccelerates upwards (m1  > m2)

ii) Case - 2
Two bodies of different masses are attached at two ends of a light string passing over a light pulley.  m1 is placed on a horizontal surface and m2 is hanging freely in air.
For vertical equilibrium m1
N = m1g
For horizontal acceleration of m1
T = m1a
For vertically downward acceleration of mT
m2g - T = m2a

iii) Case - 3
Two bodies of different masses are attached at two ends of a light string passing over a light pulley.  m1 is placed on an inclined surface and m2 is hanging freely in air
For equilibrium of mperpendicular to incline plane T
N = m1gCosθ N
For acceleration of mup the incline plane T
For vertically downward acceleration of m2

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