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JEE Main 201325 AprilOnline
Exam
JEE Main
Year
2013
Date
25 April
Mode
Online
Subject
Physics
Chapter
Mechanical Properties of Fluids

JEE Main 2013 · 25 April · Online · Physics · Mechanical Properties of Fluids

In an experiment, a small steel ball falls through a liquid at a...

In an experiment, a small steel ball falls through a liquid at a constant speed of 10 cm/s10 \mathrm{~cm} / \mathrm{s}. If the steel ball is pulled upward with a force equal to twice its effective weight, how fast will it move upward ?In an experiment, a small steel ball falls through a liquid at a constant speed of 10 ~cm / s . If the steel ball is

Options

  1. A5 cm/s5 \mathrm{~cm} / \mathrm{s}
  2. BZero
  3. C10 cm/s10 \mathrm{~cm} / \mathrm{s}
  4. D20 cm/s20 \mathrm{~cm} / \mathrm{s}

Correct answer

C. 10 cm/s10 \mathrm{~cm} / \mathrm{s}

Step-by-step solution

In an experiment, a small steel ball falls through a liquid at a constant speed of 10 ~cm / s . If the steel ball is
Weight of the body W=mg=43πr3ρg\mathrm{W}=\mathrm{mg}=\frac{4}{3} \pi \mathrm{r}^3 \rho \mathrm{g} T=43πr3σg\mathrm{T}=\frac{4}{3} \pi \mathrm{r}^3 \sigma \mathrm{g} and F=6πηvr\mathrm{F}=6 \pi \eta \mathrm{vr} When the body attains terminal velocity net force acting on the body is zero. i.e., W−T−F=0\mathrm{W}-\mathrm{T}-\mathrm{F}=0 And terminal velocity v=29r2(ρ−σ)gη\mathrm{v}=\frac{2}{9} \frac{\mathrm{r}^2(\rho-\sigma) \mathrm{g}}{\eta} As in case of upward motion upward force is twice its effective weight, therefore, it will move with same speed 10 cm/s10 \mathrm{~cm} / \mathrm{s}
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