Assuming that the mass m of the largest stone that can be moved by a flowing river depends on velocity v, show that m varies directly as the sixth power of velocity of flow.
Answers
Answer:
Given :
Heat gained = 4.5 × 10⁵ J
Heat released = 2 × 10⁵ J
To Find :
Percentage efficiency of steam engine and work done per cycle..
Solution :
❒ Efficiency of a heat engine/steam engine is given by, η = 1 - (Q₂ / Q₁)
Where,
η denotes efficiency
Q₂ denotes heat released to the sink
Q₁ denotes heat extracted from the source
By substituting the given values;
➛ η = 1 - (Q₂ / Q₁)
➛ η = 1 - (2 × 10⁵ / 4.5 × 10⁵)
➛ η = 1 - 0.44
➛ η = 0.56
Percentage efficiency = 56%
❒ Work done per cycle :
We know that work done is measured as the change in energy.
➠ W = Q₁ - Q₂
➠ W = (4.5 × 10⁵) - (2 × 10⁵)
➠ W = 2.5 × 10⁵ J
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