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Two hail stones iron the form of a sphere with radii in the ra

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Two hail stones iron the form of a sphere with radii in the ratio 1:2, fall from a great height through the atmosphere. What will be the ratio of their momenta when they attain their respective terminal velocities?

1:16

1;32

1:1

1;4

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Two hail stones iron the form of a sphere with radii in the ratio 1:2, fall from a great height through the atmosphere. What will be the ratio of their momenta when they attain their respective terminal velocities?

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Text solutionVerified

The terminal velocity is attained when gravitational force is equal and opposite is given by

v = \frac{2 r ^{2} ( ρ - σ ) g}{9 η}

. . . . . . . (1)

v \propto r^{2}

\frac{v _{1}}{v _{2}} = \frac{r _{1}^{2}}{r _{2}^{2}}

\frac{v _{1}}{v _{2}} = \frac{1 ^{2}}{2 ^{2}} = \frac{1}{4}

Mass,

m = ρ \frac{4}{3} π r^{3}

. . . . . .(2)

m \propto r^{3}

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

\frac{m _{1}}{m _{2}} = (\frac{1}{2})^{3} = \frac{1}{8}

ratio of momentum,

\frac{P _{1}}{P _{2}} = \frac{m _{1}}{m _{2}} . \frac{v _{1}}{v _{2}}

\frac{P _{1}}{P _{2}} = \frac{1}{8} . \frac{1}{4} = \frac{1}{32}

P_{1} : P_{2} = 1 : 32

The correct option is B.

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Question Text	Two hail stones iron the form of a sphere with radii in the ratio 1:2, fall from a great height through the atmosphere. What will be the ratio of their momenta when they attain their respective terminal velocities?
Answer Type	Text solution:1
Upvotes	150

Two hail stones iron the form of a sphere with radii in the ratio 1:2, fall from a great height through the atmosphere. What will be the ratio of their momenta when they attain their respective terminal velocities?

Text solutionVerified

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