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Question
(i) The diameter of neck and bottom of a bottle are 2 cm and 10 cm, respectively. The bottle is completely filled with oil. If the cork in the neck is pressed in with a force of 1.2 kgf, what force is exerted on the bottom of the bottle?
(ii) Name the law/principle you have used to find the force in part (a).
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Solution
(i) Diameter of the neck of the bottle , d1 = 2 cm
Diameter of the bottom of the bottle , d2 = 10 cm
Force on the cork in the neck , F1 = 1.2 kgf
Force on the bottom be F2
By the principle of hydraulic machine ,
Pressure on neck = pressure on bottom
or , `F_1/A_1 = F_2/A_2`
or , `1.2/(pi(d_1"/"2)^2)` = `F_2/(pi(d_2"/"2)^2)`
or , `F_2 = 1.2/(2)^2 xx (10)^2 = 30` kgf
(ii) Pascal's law has been used to find the force .
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