# In a wheel and differential axle, the diameter of the effort wheel is 400 mm. The radii of the load axles are 150mm and 100 mm respectively. The diameter of the rope is 10 mm. Find the load which can be lifted by an effort of 100 N, assuming an efficiency of the machine to be 75%.

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In a wheel and differential axle, the diameter of the effort wheel is 400 mm. The radii of the load axles are 150mm and 100 mm respectively. The diameter of the rope is 10 mm. Find the load which can be lifted by an effort of 100 N, assuming an efficiency of the machine to be 75%.

(a) 800 N

(b) 725 N

(c) 615 N

(d) none of the mentioned

This question was posed to me in final exam.

My query is from Pulleys topic in portion Belt, Rope and Chain Drives of Machine Kinematics

by (106k points)
Correct option is (c) 615 N

To explain: Diameter of effort wheel, D = 400 mm

Diameter of longer axle, d1 = 2 x 150 = 300 mm

Diameter of the smaller axle, d2 = 2 x 100 = 200 mm

Diameter of the rope, dr = 10 mm

therefore, V.R. = 2(D + dr )/(d1 + dr ) – (d2 + dr )

= 2(400 + 10)/ (300 + 10) – (200 + 10)

= 820/100 = 8.2

Effort, P = 100 N

ȵ = 75%

Let W = load which can be lifted by the machine

ȵ = M.A./V.R.

0.75 = W/P x 8.2

W = 0.75 x 100 x 8.2 = 615 N.

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