In the hydraulic pistons shown in the sketch, the small piston has a diameter of 2 cm and the large piston has a diameter of 6 cm. How much force can the larger piston exert compared with the force applied to the smaller piston?
The force exerted by larger piston in comparison to the force applied to the smaller piston.
Answer to Problem 61A
The force exerted by larger piston is 9 times more than the force applied to the smaller piston.
Explanation of Solution
Given:
The diameter of the small piston = 2cm
The diameter of the large piston = 6 cm
Formula used:
Pressure is,
Calculation:
Rearranging the above equation,
It is observed that force is proportional to area. Also, area is proportional to square of the diameter.
So, the ratio of force applied by large piston to force applied by smaller piston is
Conclusion:
Therefore, the force can the larger piston exerts is 9 times more than the force applied to the smaller piston.
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