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Mechanical proprties of solids

Two hail stones with radii in the ratio of 1:2 fall from a gre

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Two hail stones with radii in the ratio of 1:2 fall from a great height through the atmosphere. Then the ratio of their momenta after they have attained terminal velocity is:

Name: Video solution 1: Two hail stones with radii in the ratio of 1:2 fall from a great height through the atmosphere. Then the ratio of their momenta after they have attained terminal velocity is:
Uploaded: 2023-01-11T18:31:56.000Z
Duration: 12 min
Description: Video solution 1: Two hail stones with radii in the ratio of 1:2 fall from a great height through the atmosphere. Then the ratio of their momenta after they have attained terminal velocity is:

1:1

1:4

1:16

1:32

Views: 5,755 students

Updated on: Jan 11, 2023

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Two hail stones with radii in the ratio of 1:2 fall from a great height through the atmosphere. Then the ratio of their momenta after they have attained terminal velocity is:

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Text solutionVerified

p= mv
where p = momentum
m = mass
v = velocity

M a ss = d e n s i t y \times r^{3}

M a ss \propto r^{3}

Now, terminal velocity is:

v = \frac{2}{9} r^{2} g \frac{( d _{2} - d _{l} )}{n}

where
r = radius of oil drop
g = acceleration due to gravity

d_{1}

= density of body

d_{2}

= density of medium

Hence,

v \propto r^{2}

As p = m v and

m \propto r^{3}, v \propto r^{2}

Therefore

p \propto r^{5}

Hence

\frac{p _{1}}{p _{2}} = \frac{( r _{1} ) ^{5}}{( r _{2} ) ^{5}}

Now

r_{2} = 2 r_{1}

\frac{p _{1}}{p _{2}} = \frac{( r _{1} ) ^{5}}{( 2 r _{1} ) ^{5}}

\frac{p _{1}}{p _{2}} = \frac{1}{32}

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Question Text	Two hail stones with radii in the ratio of 1:2 fall from a great height through the atmosphere. Then the ratio of their momenta after they have attained terminal velocity is:
Updated On	Jan 11, 2023
Topic	Mechanical Properties of Solids
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 2
Upvotes	199
Avg. Video Duration	10 min

Two hail stones with radii in the ratio of 1:2 fall from a great height through the atmosphere. Then the ratio of their momenta after they have attained terminal velocity is:

Text solutionVerified

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Two hail stones with radii in the ratio of 1:2 fall from a great height through the atmosphere. Then the ratio of their momenta after they have attained terminal velocity is:

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