dm=σdAdxcomycom=σ(dx)(dy)=abσ0x(dx)(dy)=∫dm∫xdm=∫0abσ0(dx)(dy)∫xab(σ0x)(dx)(dy)=∫0bxdx∫0bdy∫0ax2dx∫0bdy=32a=∫dm∫ydm=∫abσ0x(dx)(dy)∫y(abσ0x)(dx)(dy) =∫0axdx∫0bdy∫0axdx∫0bydy=2b i.e., rcom≡(32a,2b)
The center of mass of a thin rectangular plate (fig - x ) with sides of length a and b, whose mass per unit area (σ) varies as σ= σ_0 x a b (where…
JEE Main 2025 — Physics Mechanics
2025mcqmedium
The center of mass of a thin rectangular plate (fig - x ) with sides of length a and b, whose mass per unit area (σ) varies as σ=abσ0x (where σ0 is a constant), would be 
Official previous-year question
Held on 28 Jan 2025 · Verified 6 Jul 2026.
Options
- A
(32a,2 b)
- B
(2a,2 b)
- C
(31a,2 b)
- D
(32a,32b)
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