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A cylinder is filled with a liquid of refractive index $μ$ . The radius of the cylinder is decreasing at a constant rate K. The volume of the liquid inside the container remains constant at V. The observer and the object O are in a state of rest and at a distance L from each other. The apparent velocity of the object as seen by the observer, (when radius of cylinder is r)

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$\frac{(1 - μ) 2 K V}{(π μ r^{3})}$

$\frac{(1 - μ) 2 K V}{(π μ L r^{2})}$

$\frac{(1 - μ) 2 K}{μ}$

$\frac{(1 - μ) K}{2 μ}$

answer is A.

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Detailed Solution

$X_{a p p} = L - H + \frac{H}{μ} \frac{d X_{a p p}}{d t} = \frac{d H}{d t} (\frac{1 - μ}{μ}) π r^{3} H = V$

$∴ \frac{d H}{d t} = - \frac{2 H}{r} \frac{d r}{d t} = \frac{2 K H}{r} ∴ \frac{d X_{a p p}}{d t} = \frac{2 K V}{π r^{3}} (\frac{(1 - μ)}{μ})$

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