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Question

A hydraulic press can lift 100kg 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.


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Solution

Step 1: Given data and assumption.

Mass on the larger piston m2=100kg

Mass on the smaller piston m1=m

Let mass m also lift the mass in second case be M0

Step 2: Finding the mass M0 on the larger piston in second case.

Using Pascal Law:

ρ0+m1gA1=ρ0+m2gA2

Where, ρ0=atmospheric pressure, A1=A2=area of piston, g=acceleration due to gravity.

Now,

From figure:a

ρ0+mgA1=ρ0+100×gA2

mgA1=100×gA2 ….i

Again,

From figure:b

Mass m on smaller piston can lift M0 on the larger piston in second case

Diameter of larger piston is increased by 4 times then new area is,

A2=16A2 A=πd24

Diameter of smaller piston is decreased by 4 times then new area is,

A1=A116

Therefore,

ρ0+mgA116=ρ0+M0×g16A2

mgA1=M0×g16×16A2 ….ii

From equation i and ii we get.

M0×g16×16A2=100×gA2

M0=25600kg

Hence, It can lift 25600 kg


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