Find the distance (cm) of the centre of mass from O for the uniform bent plate shown: a 2 cm × 4 cm vertical strip joined to a 12 cm × 2 cm horizontal strip.
Physics · Mixed Chapter
JEE Main Practice

Question

Find the distance (cm) of the centre of mass from O for the uniform bent plate shown: a 2 cm × 4 cm vertical strip joined to a 12 cm × 2 cm horizontal strip.

G1 Physics · Accepted Answer

Step 1: Treat the L-shape as non-overlapping rectangles measured from O: vertical strip area A₁ = 2×4 = 8 cm², with x₁ = 1 cm. Step 2: Horizontal rectangle to the right of strip has area A₂ = 12×2 = 24 cm², with centroid x₂ = 2+12/2 = 8 cm. Step 3: Centre-of-mass x-coordinate xcm = (A₁x₁+A₂x₂)/(A₁+A₂) = (8×1+24×8)/32 = 6.25 cm.