A bottle completely filled with water is corked. The areas of the mouth and the bottom of the bottle are `10cm^(2)` and `100cm^2` respectively and the height of the bottle is 40 cm. If the cork is pressed with a 10 N force, then calculate the total thrust on its bottom.

Explanation

Area of cross-section of the cork = `10cm^(2)` , area of the bottom of the bottle = `100cm^(2)`.
Pressure on the cork = `1 N*cm^(-2)`.
According to Pascal.s law, the pressure exerted on the bottom of the bottle, `p=1N*cm^(-2)`.
`therefore` Thrust on the bottom of the bottle due to the applied pressure,
`F_(1)=1xx100=100N`
Thrust on the bottom of the bottle due to the water in it,
`F_(2)=hrhogxxA`
Here, `h=40cm=0.4m,rho=10^(3)kg*m^(-3),g=9.8m*s^(-2)`,
`A=100cm^(2)=10^(-2)m^(2)`
`therefore" "F_(2)=0.4xx10^(3)xx9.8xx10^(-2)=39.2N`
`therefore` Total thrust on the bottom
`=F_(1)+F_(2)=100+39.2=139.2N`