A piston of mass M=3kg and radius R=4cm has a hole into which a thin pipe of radius r=1 cm is inserted the piston can enter a cylinder tightly and without friction an initially it is at the bottom of the cylinder 750 gm of water is now poured into the pipe so that the piston&pipe and lifted up as shown find the height H of water in the cylinder and height h of water in the pipe.

Answer

`(2m)/(pi)`,`H=(11)/(32pi)m`

Explanation

For `h`
`P+(mg)/(pi(R^(2)-r^(2)))=P+hrhog`
`hrhog=(mg)/(pi(R^(2)-r^(2)))`
`h=(m)/(pi(R^(2)-r^(2))rho)`
`h=(3)/(rho[(4xx10^(-2))^(2)-(1xx10^(-2))^(2)]xx1000)`
`h=(30)/(15pi)m implies h=(2)/(pi)m`
For `H`
mass of water in cylinder `+` mass in pipe = `750gm`
`piR^(2)Hrho+pir^(2)hrho = 750`
`pixx(4)^(2)xxHxx1+pixx1^(2)xx(200)/(pi)xx1=750`
`16piH = 550`
`H=(550)/(16pi)cm " "h=(1100)/(32pi)cm implies H=(11)/(32pi)m`