A ball reads (4.00 ± 0.02) N on a spring balance in air and (1.00 ± 0.02) N in water. If maximum percentage error in relative density is P/6%, find P (approximately).
Physics · Mixed Chapter
JEE Main Practice

Question

A ball reads (4.00 ± 0.02) N on a spring balance in air and (1.00 ± 0.02) N in water. If maximum percentage error in relative density is P/6%, find P (approximately).

G1 Physics · Accepted Answer

Step 1 — Relative density D = Wₐ/(Wₐ−Ww) = 4/3. Step 2 — Both readings are individually uncertain; use partial derivatives of D rather than counting Wₐ twice independently. Step 3 — ∂D/∂Wₐ = −Ww/(Wₐ−Ww)² = −1/9; ∂D/∂Ww = Wₐ/(Wₐ−Ww)² = 4/9. Step 4 — Maximum absolute δD = (1/9)(0.02) + (4/9)(0.02) = 0.1/9. Step 5 — Percentage δD/D ×100 = [(0.1/9)/(4/3)]×100 = 5/6%. Hence P = 5.