Maximum percentage errors in the mass and density of a cube are 2% and 1%. Find the maximum percentage error in its edge length.
Physics · Mixed Chapter
JEE Main Practice

Question

Maximum percentage errors in the mass and density of a cube are 2% and 1%. Find the maximum percentage error in its edge length.

G1 Physics · Accepted Answer

Step 1: Cube density ρ=m/ℓ³, so ℓ=(m/ρ)¹⁄³. Step 2: Maximum relative error is Δℓ/ℓ=(1/3)(Δm/m+Δρ/ρ). Step 3: Percentage error =(2+1)/3=1%.