A hydraulic press can lift 100 kg when a mass 'm' is placed on the smaller piston. It can lift _____kg when the diameter of the larger piston is increased by 4 times and that of the smaller piston is decreased by 4 times keeping the same mass 'm' on the smaller piston.

Answer

25600

Explanation

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Atmospheric pressure ` P_(0)` will be acting on both the limbs of hydraulic lift
Applying Pascal.s law for same liquid level
`rArr P_(0) + (mg)/(A_(1))= P_(0) + ((100 ) g)/( A_(2))`
`rArr (mg)/( A_(1)) = ((100) g)/( A_(2)) rArr (m)/(100) = (A_(1))/(A_(2))` . . . (i)
Diameter of piston on side of 100 kg is increased by 4 times so new area ` = 16 A_(2)`
Diameter of piston on side of (m) kg is decreasing
`A_(2)` = (A_(1))/(16)`
(In order to increasing weight lifting capacity, diameter of smaller piston must be reduced )
Again `(mg)/(((A_(1))/(16)))= (M.g)/(16 A_(2))`
`rArr (256 m)/( M.) = (A_(1))/(A_(2)) ` [ here M. = new weight lifting capacity]
from equation (i) = `(256 m)/( M.) = (m)/(100) rArr M. = 25600 kg `