SATHEE: Optics Question 135

Optics Question 135

Question: The apparent depth of water in cylindrical water tank of diameter 2R cm is reducing at the rate of x cm/minute when water is being drained out at a constant rate. The amount of water drained in c.c. per minute is (n1 = refractive index of air, n2 = refractive index of water)

[AIIMS 2005]

Options:

A) x p R2 n1/n2

B) x p R2 n2/n1

C) 2 p R n1/n2

D) p R2 x

Show Answer

Answer:

Correct Answer: B

Solution:

Apparent depth $h^{'} = \frac{h}{_{a i r} μ_{l i q u i d}}$

Therefore $\frac{d h^{'}}{d t} = \frac{1}{_{a} μ_{w}} = \frac{1}{_{a} μ_{w}} \frac{d h}{d t}$

Therefore $x = \frac{1}{_{a} μ_{w}} \frac{d h}{d t}$

Therefore $\frac{d h}{d t} =_{a} μ_{w} x$ Now volume of water $V = π R^{2} h$

Therefore $\frac{d V}{d t}$

$= π R^{2} \frac{d h}{d t}$

$= π R^{2} ._{a} μ_{w} x$

$=_{a} μ_{w} π R^{2} x$

$= \frac{μ_{w}}{μ_{a}} π R^{2} x$

$= (\frac{n_{2}}{n_{1}}) π R^{2} x$

Optics Question 135

Question: The apparent depth of water in cylindrical water tank of diameter 2R cm is reducing at the rate of x cm/minute when water is being drained out at a constant rate. The amount of water drained in c.c. per minute is (n1 = refractive index of air, n2 = refractive index of water)

Options:

Answer:

Solution:

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Optics Question 135

Question: The apparent depth of water in cylindrical water tank of diameter 2R cm is reducing at the rate of x cm/minute when water is being drained out at a constant rate. The amount of water drained in c.c. per minute is (n1 = refractive index of air, n2 = refractive index of water)

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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