A cylindrical vessel is filled with water upto the height 1 m from the base. A small orifice is opened at some height in the cylinder and the water level is reduced to height of orifice in 20 s. If the base area of the cylinder is 100 times the area of orifice, then the height of orifice from the base is (take, `g = 10 m//s ^(2))`

Options

A. 80 cm
B. 60 cm
C. 40 cm
D. 20 cm

Answer

A

Explanation

Height of water in vessel =1 m
Let orifice is at a depth h from above

Time taken to raduce the water level up to orifice,
`t = (A)/(A _(0)) sqrt((2x )/(g))`
where, ` A_(0) =` area of orifice and `A = ` base area.
Given, `(A)/(A_(0)) =100, t = 20 s implies 20 =100 sqrt((2x)/(10))`
`sqrt((x)/(5)) =1/5implies x= 1/5 = 0.2m or 20 cm`
Now, height of orifice from base,
`h = 100- 20 = cm`