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Question
What should be the ratio of area of cross section of the master cylinder and wheel cylinder of a hydraulic brake so that a force of 15 N can be obtained at each of its brake shoe by exerting a force of 0.5 N on the pedal ?
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Solution
Let the ratio of area of cross - section of the master cylinder and wheel cylinder be A1 : A2
Force on pedal , F1 = 0.5 N
Force on break shoe , F2 = 15 N
By the principle of hydraulic machine,
Pressure on narrow piston = pressure on wider piston
or , `F_1/A_1 = F_2/A_2`
or , `F_1/F_2 = A_1/A_2`
or , `A_1/A_2 = 0.5/15`
or , `A_1/A_2 = 1/30`
Thus , the required ratio is 1:30
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