To lift an automobile of 5000kg, a hydraulic lift with a large piston 800cm2 in area is employed. Calculate the force that must be applied to a small piston of area 5cm2 to achieve it.
A
612.5N
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B
306.25N
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C
153.12N
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D
408.56N
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Solution
The correct option is B306.25N Force on large pistion (F1)=mg F1=5000×9.8N=4.9×104N
Given area of large piston, A1=800cm2
Pressure on the large pistion (P)= F1A1=4.9×104800×10−4=6.125×105Pa
Since the liquid transmits pressure equally, therefore the pressure on the small piston will be equal to the pressure on the large pistion. F1A1=F2A2=P
Given area of small pistion A2=5cm2 ∴ Force applied on small pistion(F2)=P×A2 =6.125×105×(5×10−4)=306.25N