Three identical steel rods of length 2 m form an equilateral triangle ABC, with the origin at midpoint O of horizontal side BC and vertex A on positive y-axis. Coefficient of linear expansion is 4√3×10⁻⁶ °C⁻¹. If the rise in y-coordinate of the centre of mass per degree Celsius is n×10⁻⁶ m, find n.
Physics · Mixed Chapter
JEE Mains

Question

Three identical steel rods of length 2 m form an equilateral triangle ABC, with the origin at midpoint O of horizontal side BC and vertex A on positive y-axis. Coefficient of linear expansion is 4√3×10⁻⁶ °C⁻¹. If the rise in y-coordinate of the centre of mass per degree Celsius is n×10⁻⁶ m, find n.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Centre of mass of three identical uniform rods: Each rod has the same mass; the centre of mass of the wire frame is the average of their midpoints, which is the triangle centroid. Its y-coordinate equals h/3 above BC. Step 2 — Triangle altitude: h = (√3/2)l = √3 m for l = 2 m. Thus y = h/3 = √3/3 m. Step 3 — Thermal expansion of the complete similar frame: The fractional increase in every length and in y is αΔT. Therefore dy/dT = α y = (4√3×10⁻⁶)(√3/3) = 4×10⁻⁶ m °C⁻¹. Step 4 — Coeffic…