cm

Find distance of centre of mass of a uniform plate having inner and outer boundaries as a and b........

3 Answers

arey do it the way we do for semicircular plate re.........

take a ring first. ... uske liye com ka expression likho..

then integrate it from a to b. :)

nahi toh aur ek method bhi hai... widout integration...

com of a semicircular plate wid radius a - com of semicircular plate wid radius b.

i mean the way we find com of a plate afetr cutting out a section from it..

it will be frm Sky's 2 method..

COM from center (frm where a and b is measured in fig) be x in the line of symmetry..

then from sky's 2 method..
Ï is density..

Ï€a²/2Ï(4a/3Ï€)+(Ï€/2Ï(b²-a²)x =4b/3Ï€
Ï€b²Ï/2

solve for x..

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

∑ ∑ ∑ ∑ ∑ ∮ ∮ ∮ ∮ ∮ ∏ ∏ ∏ ∏ ∏ ∐ ∐ ∐ ∐ ∐

+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω