Question

The drag force of flowing water of river on a spherical stone in the river depends only on density of the water, its flow speed and radius of the stone. Ratio of the drag forces on two spherical stones of radii 10 cm and 20 cm would be

Answer 1

Answer:

1:4 is your answer

hope this would help you

Explanation:

M=1,Y=2

-3m+y+z=1

-3+2+z=1

-1+z=1

Z=2

F=K  V^2   R^2

(F^1/F^2)=(V^2 x 10 x 10/v^2 x 20 x 20)=1:4

Answer 2

Answer:

Dimension analysis

Explanation:

• Dimensional analysis is also known as Unit factor method or Factor-Label method.

• It is defined as the method used for problem solving and it uses the fact of any number or other expression to be multiplied by one without changing of any values.

• It also helps in checking the relations of physical quantities related to their units of measurement and their dimensions given.

Given that:

The Drag force flowing in water of river in a spherical stone.

Depending on density of water, flow speed and radius of a stone,

The two spherical stone with radii = 10 cm and 20 cm

To find: Ratios of two spherical stones =?

Solution:

Formula to be applied,

$F= [Density^{x} ] [Velocity^{y} ] [radius^{z} ]$

$M^{1} L^{1} T^{-2}$

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

comparing both the sides, we get,

x=1  --------------(1)

-3x+y+z =1  ------------(2)

-2 = -y -------------- (3)

By solving all equation (1), (2) and (3), we get,

x=1 , y = 2, z =2

$F = [Density^{1} ] [Velocity^{2} ] [radius^{2} ]$

Therefore,

$F_{1} / F_{2} = [Density^{1} ] [Velocity^{2} ] [radius^{2} ] / [Density^{1} ] [Velocity^{2} ] [radius^{2} ]$

Here, density and velocity will be same value. So we get,

$F_{1} / F_{2} = r_{1}^{2} / r_{2} ^{2}$

$F_{1} / F_{2} = 10^{2} / 20^{2}$

$F_{1} / F_{2} = 1 / 4$

Therefore, the ratio is 1:4

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