The neck and bottom of a bottle are 2 cm and 20 cm in diameter respectively if the cork is pressed with a force of 1.2 kgf in the neck of the bottle, calculate the force exerted on the bottom of the bottle.

Answer

120 kgf

Explanation

`2 r_1 = 2cm or r_1 =1 cm`
and `2 r_2 = 20 cm or r_2 =10 cm , `
`A_1= pi r_1^2 and A_2 = pi r_2^2 ,`
`F_1 = 1.2 kg f = 1.2 xx 9.8 N ,`
`F_2 = (F_1)/(A_1)xxA_2 = (1.2xx9.8)/(pi r_1^2) xx pi r_2^2 = 1.2 xx 9.8 xx r_2^2 // r_1^2`
` = 1.2 xx 9.8 xx (10)^2//(1)^2 = 1.2 xx 9.8 xx 100 N`
= 120 kg.f`