KVPY 2020-21 SA Exam Previous Papers

Question : 70 of 80

Marks: +1, -0

A small coin is fixed at the centre of the base of an empty cylindrical steel container having radius R = 1 m and height d = 4 m. At time t = 0 s, the container starts getting 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 the 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 is n = 1.33

0 s
32 s
63 s
150 s

Validate

Solution:

R = 1
L = 1.5 m
d = 4 m

\tan r={L-R}/{H-d}={2}/{7}={x}/{d-h}

\tan i={R-x}/{h}

Using Snell’s Law

\µ\sin i=\sin r \⇒\tan i={3}/{\√{203}}

x=(d-h) \tan r=R-h \tan i

\⇒h={d \tan r-R}/{\tan r-\tan i}=1.9 {m}

Volume

=\π r^{2} h=3.14 \×1.9

t={3.14 \×1.9}/{0.1}=60 {s}

Most appropriate answer is

63 {s}

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