The velocity ratio of a third system of pulleys with four pulleys is-

Concept:

Third system of pulleys

• The figure shows the third system of the pulley.
• In this system, several movable pulleys are arranged, keeping the topmost pulley fixed.
• The number of strings is equal to the number of pulleys.
• One end of each string is attached to a common block, to which load is attached.
• The other end of each string, passing around the periphery of the pulley, is fastened to the block of the next lower pulley.
• The effort is applied to the free end of the lowermost pulley.
• Neglecting friction and weight of pulleys, the equilibrium of the system gives
• W = T₁ + T₂ + T₃ + T₄
• But from the equilibrium of pulleys 1, 2, 3, 4, we have 
• If there are 'n' pulleys, then 
• This is a geometrical progression, 
• ∴ 
• For an ideal machine, 
• ∴ VR = MA = 
• VR = 2ⁿ - 1

Calculation:

GIven:

n = 4

VR = 2n - 1

VR = 2⁴ - 1 = 15