A drum of 40 cm radius has a capacity of 440 `dm^(3)` of water. It contains 396 `dm^(3)` of water and is placed on a solid block of exactly the same size as of drum. If a small hole is made at lower end of the drum perpendicular to its length, find the horizontal range of water on the ground in the beginning. Given `g=10m//s^(2)`

Explanation

Radius of drum, `r=40cm`
Volume of the drum `=440dm^(3)`
`=4.4xx10^(5)cm^(3)`
`[thereforedm=0.1m=10cm]`

If h is the height of the drum, then
`pir^(2)h=4.4xx10^(5)`
(or) `h=(4.4xx10^5)/((22//7)xx40xx40)`
`=87.5cm` Height of block,
`h_(1)=h=87.5cm`
Volume of water `=396dm^(3)`
`=3.96xx10^(5)cm^(3)`
Let `h_(2)` be the height of the water column in the drum. Then
`pir^(2)h^(2)=3.96xx10^(5)`
`h_(2)=(3.96xx10^(5))/((22//7)xx(40)^(2))=78.75cm`
Time taken by water to reach the ground,
`t=sqrt((2h_1)/(g))`
Velocity of efflux of water,
`V=sqrt(2gh_2)`
Horizontal range,
`R=Vt=sqrt(2gh_2)xxsqrt((2h_1)/(g))`
`=2sqrt(h_(1)h_(2))`
`=2sqrt(87.5xx78.75)=166cm`