Question

the drag force of flowing water of River on a spherical stone in the river depends only on density of the water is closed speed and radius of the stone ratio of the drag force on two spherical stone of Reddy 10 cm and 20 CM​

Answer 1

1:4 is your answer

hope this would help you

Answer 2

This question can be solved by dimension analysis.

Dimension Analysis : Dimensional analysis is the practice of checking relations amongst physical quantities by identifying their dimensions and units of measurement.

Given :  Drag force of flowing water of River on a spherical stone in the river depends only on density of the water.

To find : Ratio of drag force on radius of  10 cm and 20 cm stone.

Solution : $F = [ density ]^{x} [ velocity ]^{y} [ radius ]^{z}$

                 $M ^{1} L^{1} T^{-2} = M^{x} L^{-3x + y +z} T^{-y}$

                  Compare both sides power of same unit.

                 we get, x =1 ________________(1)

                             -3x + y + z = 1 _________(2)

                              -2 = -y ______________(3)

On solving equation (1), (2) and (3)

We get, x = 1

            y = 2

            z = 2

$F = density^{1} velocity^{2} radius^{2}$

$\frac{F_{1} }{F_{2} } = \frac{ density^{1}_{1} velocity^{2}_{1} radius^{2}_{1}}{density^{1}_{2} velocity^{2}_{2} radius^{2}_{2}}$

Density and velocity are same. So, these are cancel out.

$\frac{F_{1} }{F_{2} } = \frac{r^{2}_{1} }{r^{2}_{2} }$

$\frac{F_{1} }{F_{2} } = \frac{10^{2} }{20^{2} }$

$\frac{F_{1} }{F_{2} } = \frac{1}{4}$

Hence ratio is 1 : 4

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