Question

Q6. Assuming that the mass m of the largest stone that can be moved by a flowing river depends on the velocity v, the density of water ρ and acceleration due to gravity g. Show that m varies as the sixth power of the velocity of flow

Need step by step solution
. ​

Answer 1

From Given:-

since Mass ∝V

a

d

b

g

c

⇒M=kV

a

d

b

g

c

Equating dimensions.

[M

′

]=k[L

1

T

−1

]

a

[ML

−3

]

b

[L

1

T

−2

]

c

⇒ on comparing:-

b=1,a−3b+c=0

⇒a+c=3......(1)

and −a−2c=0......(2)

on solving:-

c=−3 and a=6

∴M=k

g

3

V

6

d

∴ Mass ∝ sixth Power of Velocity

Hope it helps

plzzz mark as brainliest ✌️ ✌️✌️✌️

Answer 2

Answer:

      m ∝ v⁶.ρ¹.g⁻³

Explanation:

m ∝ vᵃ.ρᵇ.gˣ

vᵃ = [L¹T⁻¹]ᵃ

ρᵇ = [M¹L⁻³]ᵇ

gˣ = [L¹T⁻²]ˣ

Using dimensional analysis

[M¹L⁰T⁰] ∝ [L¹T⁻¹]ᵃ.[M¹L⁻³]ᵇ. [L¹T⁻²]ˣ

[M¹L⁰T⁰] ∝ [Lᵃ⁻³ᵇ⁺ˣ].[T⁻ᵃ⁻²ˣ].[M]ᵇ

[M¹] ∝ [M]ᵇ

b = 1

[L⁰] ∝[Lᵃ⁻³ᵇ⁺ˣ]

a - 3b + x = 0

a - 3 + x = 0

a + x = 3 -----{i}

[T⁰] ∝ [T⁻ᵃ⁻²ˣ]

-a - 2x = 0 ----{ii}

add {i} and {ii}

a + x - a - 2x = 3

x - 2x = 3

-x = 3

x = -3

a - 3 = 3

a = 6

b = 1 , x = -3 , a = 6

m ∝ vᵃ.ρᵇ.gˣ

m ∝ v⁶.ρ¹.g⁻³

m ∝ v⁶