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(i) An effort is applied on the bigger wheel of a gear having 32 teeth. It is used to turn a wheel of 8 teeth. Where is it used?

(ii) A pulley system has three pulleys. A load of 120 N is overcome by applying an effort of 50 N. Calculate the Mechanical Advantage and Efficiency of this system.

Machines

ICSE 2016

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Answer

(i) In a gear system, the wheel on which effort is applied is called driving gear and other one is called driven gear. If number of teeth are more in driving gear than the driven gear, then we gain in speed.

(ii) Given, Load = 120 N and E = 50 N,

From relation,

M.A.=LE\text{M.A.} = \dfrac{\text{L}}{\text{E}}

Substituting the values in the formula above we get,

M.A.=12050⇒M.A.=2.4\text{M.A.} = \dfrac{120}{50} \\[0.5em] \Rightarrow \text{M.A.}= 2.4

V.R. = 3

Efficiency (η)=M.A.V.R.×100%\text{Efficiency (η)} = \dfrac{\text{M.A.}}{\text{V.R.}} \times 100\%

Substituting the values in the formula above we get,

η=2.43η=80\text{η} = \dfrac{2.4}{3}\% \\[0.5em] \text{η} = 80\%

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