A small coin is fixed at the center 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 .

Question

A small coin is fixed at the center 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

MARKS App · Accepted Answer

1 . 33 sin i = sin r = 2 53 . . . ( i ) Also, tan r = 2 7 = 1 - y 4 - x ⇒ y = 2 x - 1 7 . . . ( ii ) ∴ From equation ( i ) ⇒ 89 . 7517 y 2 = 4 x 2 ⇒ y = 2 x 89 . 7517 . . . ( iii ) From equation ( ii ) and ( iii ) , 2 x - 1 7 = 2 x 89 . 7517 ⇒ 14 x = 2 x - 1 9 . 47 ∴ x = 1 . 92 ∴ volume of water filled = π R 2 x = 3 . 14 × 1 2 × 1 . 92 m 3 ∴ Q t = 6 . 0288 [ Q is volume flow rate] ∴ t = 60 . 288 sec so option C is the nearest value

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