A mercury U-tube has column heights 100 cm at 0°C and 101.8 cm at 100°C. If coefficient of real cubical expansion is 3x×10⁻⁵ °C⁻¹, find x.
Physics · Mixed Chapter
JEE Main Practice

Question

A mercury U-tube has column heights 100 cm at 0°C and 101.8 cm at 100°C. If coefficient of real cubical expansion is 3x×10⁻⁵ °C⁻¹, find x.

G1 Physics · Accepted Answer

Step 1: At same bottom level hydrostatic pressure is equal: ρ₀g(100)=ρ₁₀₀g(101.8). Step 2: As ρ₁₀₀=ρ₀/[1+β(100)], equality gives 101.8/100=1+100β. Step 3: β=(1.018−1)/100=1.8×10⁻⁴ °C⁻¹=18×10⁻⁵ °C⁻¹. Step 4: Given β=3x×10⁻⁵, hence 3x=18⇒x=6.