assuming that mass,m of the largest store that can be moved by a flowing river depends on velocity of water,its density p and acceleration due to gravity g,then m is directly proportional to ?
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hello here's ur answer
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Narain007:
but the options are a) v power6 b)v power5 c)v power4 d)v
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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
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