Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • The apparent depth of water in cylindrical water tank of diameter cm in reducing at the rate of <im

The apparent depth of water in cylindrical water tank of diameter \mathrm{2R} cm in reducing at the rate of \mathrm{x} \mathrm{cm/min} when water is being drained out at a constant rate. The amount of water drained in \mathrm{cc/min} is ( \mathrm{n_{1}=} refractive index of air, \mathrm{n_{2}=} refractive index of water)

Option: 1

\mathrm{\frac{\mathrm{x} \pi \mathrm{R}^2 \mathrm{n}_1}{\mathrm{n}_2}}


Option: 2

\mathrm{\frac{\mathrm{x} \pi \mathrm{R}^2 \mathrm{n}_2}{\mathrm{n}_1}}


Option: 3

\mathrm{\frac{2 \pi \mathrm{R}^2 \mathrm{n}_1}{\mathrm{n}_2}}


Option: 4

\mathrm{\pi R^2 x}


Answers (1)

best_answer

\mathrm{\text { As } \mathrm{y}_{\mathrm{a}}=\left(\frac{\mathrm{n}_1}{\mathrm{n}_2}\right) \mathrm{y}}
Here, \mathrm{y=} actual depth
and \mathrm{y_{a}=} apparent depth
\mathrm{\therefore \quad \mathrm{y}=\left(\frac{\mathrm{n}_2}{\mathrm{n}_1}\right) \cdot \mathrm{y}_{\mathrm{a}} \Rightarrow\left(-\frac{\mathrm{dy}}{\mathrm{dt}}\right)=\frac{\mathrm{n}_2}{\mathrm{n}_1}\left(-\frac{\mathrm{dy}_{\mathrm{a}}}{\mathrm{dt}}\right)=\frac{\mathrm{n}_2 \mathrm{x}}{\mathrm{n}_1}}
The amount of water drained in \mathrm{cc/min}
\mathrm{\therefore \frac{\mathrm{dv}}{\mathrm{dt}}=\mathrm{A} \cdot\left(-\frac{\mathrm{dy}}{\mathrm{dt}}\right)=\frac{\pi \mathrm{R}^2 \mathrm{n}_2 \mathrm{x}}{\mathrm{n}_1}}

Posted by

seema garhwal

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

75% criteria for JEE Main 2025 not removed; eligibility criteria for admission to IITs
anam-khan

BTech Admissions 2025 LIVE: AEEE phase 1 exam date out, JEE Mains registration ongoing; BITSAT, VITEEE updates
anam-khan

JEE Main 2025 Eligibility Criteria: What is state code of eligibility? Here’s list of qualifying exams

Latest Question