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Terminal velocity

A small metal ball of mass 'm' is dropped in a liquid containe

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A small metal ball of mass ' $m$ ' is dropped in a liquid contained in a vessel, attains a terminal velocity ' $V$ '. If a metal ball of same material but of mass $^{'} 8 m^{'}$ is dropped in same liquid then the terminal velocity will be.

V

2 V

4 V

8 V

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A small metal ball of mass '

m

' is dropped in a liquid contained in a vessel, attains a terminal velocity '

V

'. If a metal ball of same material but of mass

^{'} 8 m^{'}

is dropped in same liquid then the terminal velocity will be.

14 mins ago

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14 mins ago

Text solutionVerified

Terminal velocity of the ball,

V = \frac{2 g r ^{2} ( ρ - σ )}{9 η}

where

ρ

and

σ

are the density of ball and liquid, respectively.
Mass of the metal ball

m = ρ (\frac{4 π}{3} r^{3})

\Rightarrow r \propto m^{1/3}

But from equation (1), we get

V \propto r^{2}

\Rightarrow V \propto m^{2/3} ......(2)

Given:

V_{1} = V, m_{1} = m, m_{2} = 8 m

From (2) we get

\frac{V _{2}}{V _{1}} = (\frac{m _{2}}{m _{1}})^{2/3}

Or \frac{V _{2}}{V} = (\frac{8 m}{m})^{2/3} = 8^{2/3}

\Rightarrow V_{2} = (2^{3})^{2/3} V = 4 V

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Question Text	A small metal ball of mass ' $m$ ' is dropped in a liquid contained in a vessel, attains a terminal velocity ' $V$ '. If a metal ball of same material but of mass $^{'} 8 m^{'}$ is dropped in same liquid then the terminal velocity will be.
Topic	Mechanical Properties of Fluids
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	107

A small metal ball of mass ' $m$ ' is dropped in a liquid contained in a vessel, attains a terminal velocity ' $V$ '. If a metal ball of same material but of mass $^{'} 8 m^{'}$ is dropped in same liquid then the terminal velocity will be.

Text solutionVerified

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A small metal ball of mass ' $m$ ' is dropped in a liquid contained in a vessel, attains a terminal velocity ' $V$ '. If a metal ball of same material but of mass $^{'} 8 m^{'}$ is dropped in same liquid then the terminal velocity will be.