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Two pistons of hydraulic press have diam...

Two pistons of hydraulic press have diameter of `30.0 cm` and `2.5 cm`, find the force exerted on the longer piston when 50.0kg wt. is placed on smaller piston.

Text Solution

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`A_(1)=pi (2.5//2)^(2) cm^(2), A_(2)=pi(30//2)^(2) cm^(2), F_(1)=50kg wt`.
Now , `F_(2)=(F_1)/(A_1) xx (A_2) = (50 xx pi xx (30//2)^(2))/(pi(2.5//2)^(2)) = (50 xx 30 xx 30 )/(2.5 xx 2.5) = 7200kg wt`.
In one stroke, Input workdone = output workdone
so, `F_(1)l_(1)=F_(2)l_(2) or l_(2)=(F_(1)l_(1))/(F_2) = (50 xx 4)/(7200) = 0.028 cm`
Disatance covered after 10 strokes = `0.028 xx 10 = 0.28 cm`.
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