Объяснение:
Дано:
m₁ = m₂ = m
d₁ = 2d
d₂ = d
-------------------------
Найти:
R₂/R₁ - ?
Решение:
R₁ = ρэ × l₁/S₁ m₁ = ρV = ρS₁l₁ | ⇒ l₁ = m₁/ρS₁
R₂ = ρэ × l₂/S₂ m₂ = ρV = ρS₂l₂ | ⇒ l₂ = m₂/ρS₂
S₁ = πR₁² = π×d₁²/4 = π×4d²/4 = πd²
S₂ = πR₂² = π×d₂²/4 = πd²/4
R₂/R₁ = ρэ × l₂/S₂ / ρэ × l₁/S₁ = l₂/S₂ × S₁/l₁ = m₂/ρS₂ × S₁ / S₂ × m₁/ρS₁ ⇒
R₂/R₁ = m×S₁/ρ×S₂ ÷ S₂×m/ρ×S₁ = m×S₁×ρ×S₁/ρ×S₂×S₂×m = S₁²/S₂² = (πd²)² ÷ (πd²/4)² = π²d⁴ ÷ π²d⁴/16 = π²d⁴×16/π²d⁴ = 16
Ответ: в 16 раз
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Answers & Comments
Объяснение:
Дано:
m₁ = m₂ = m
d₁ = 2d
d₂ = d
-------------------------
Найти:
R₂/R₁ - ?
Решение:
R₁ = ρэ × l₁/S₁ m₁ = ρV = ρS₁l₁ | ⇒ l₁ = m₁/ρS₁
R₂ = ρэ × l₂/S₂ m₂ = ρV = ρS₂l₂ | ⇒ l₂ = m₂/ρS₂
S₁ = πR₁² = π×d₁²/4 = π×4d²/4 = πd²
S₂ = πR₂² = π×d₂²/4 = πd²/4
R₂/R₁ = ρэ × l₂/S₂ / ρэ × l₁/S₁ = l₂/S₂ × S₁/l₁ = m₂/ρS₂ × S₁ / S₂ × m₁/ρS₁ ⇒
R₂/R₁ = m×S₁/ρ×S₂ ÷ S₂×m/ρ×S₁ = m×S₁×ρ×S₁/ρ×S₂×S₂×m = S₁²/S₂² = (πd²)² ÷ (πd²/4)² = π²d⁴ ÷ π²d⁴/16 = π²d⁴×16/π²d⁴ = 16
Ответ: в 16 раз