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

Explanation

Radius of durm r= ` 40 cm`
Volume of the drum = `440 dm^(3)`
`= 4.4xx10^(5) cm^(3)`
`{ ,gt 1 dm = 0.1 m = 10 cm]`

If h is the height of the durm, then
`pi r^(2) h = 4.4 xx 10^(5)`
or ` h=(4.4 xx 10^(5))/((22//7) xx 40 xx 40) = 87.5 cm`
Height of block, `h_(1) = h = 87.5 cm`
Volume of water = `396 dm^(3) = 3.96 xx 10^(5) cm^(3)`
Let ` h_(2)` be the water column in the drum. then `pi r^(2) h_(2) = 3.96 xx 10^(5)`
`h_(2) = (3.96 xx 10^(5))/((22//7)xx (40)^(2)) = 78.75 cm`
Time taken by water to reach the round
`t= sqrt((2h_(1))/(g))`
Velocity of efflux of water, `upsilon = sqrt(2 gh_(2))`
Horizontal range,
`R = upsilon t = sqrt(2 gh_(2)) xx sqrt((2h_(1))/(g)) = 2 sqrt(h_(1)h_(2))`
`= 2 sqrt(87.5 xx 78.75) = 166 cm`.