A small coin is fixed at the center of the base of an empty of cylindrical stell container having radius R = 1 m and height d = 4 m . At time t = 0 s, the container starts gettting filled with water at a flowrate of `Q= 0.1 m^3//s` without disturbing the coin . Find the approximate time when the coin will first be seen by teh observer "O" from the height of H= 5.75 m above and L = 1.5 m radially away from the coin as shown in the figure. Refractive index of water in n = 1.33

Options

A. 0 s
B. 32 s
C. 63 s
D. 150 s

Answer

C

Explanation

`1.33sini = sin r =2/(sqrt53….(i)`
Also, tan` r =2/7=(1-y)/(4-x)rArry=(2x-1)/(7...(iii))
`therefore From equation (i)
`(1.33y)/(sqrt(y^2+x^2))=2/(sqrt53)rArr(1.33)^(2)53y^(2)=4(x+^2y)^2`
`rArr89.7517y^2=4x^2rArry=(2x)/(sqrt(89.7517)).....(iii)`
From equation (ii) & (iii),
`(2x-1)/7=(2x)/(sqrt(89.7517))rArr14x=(2x-1)9.47`
`therefore x=1.92`
`therefore "volume of water filled"=piR^2X=(3.14xx1^2xx1.92)m^3`
`therefore` Qt = 6.0288 [Q is volume flow rate]
`therefore` t = 60.288 sec
so option C is the nearest value