MHTCET 25 Apr 2025 Shift 1 Paper

Concept:Density is mass divided by volume; for a wire, volume is $\pi r^2 L$.The maximum percentage error in density is the sum of percentage errors in mass, radius (with factor 2), and length.Explanation:Given: $\Delta m = 0.003$ g, $m = 0.3$ g, $\Delta r = 0.005$ mm, $r = 0.5$ mm, $\Delta L = 0.06$ cm, $L = 6$ cm.Percentage error in mass: $\frac{\Delta m}{m} \times 100 = \frac{0.003}{0.3} \times 100 = 1\%$.Percentage error in radius: $\frac{\Delta r}{r} \times 100 = \frac{0.005}{0.5} \times 100 = 1\%$.Since radius is squared in volume, its contribution is $2 \times 1\% = 2\%$.Percentage error in length: $\frac{\Delta L}{L} \times 100 = \frac{0.06}{6} \times 100 = 1\%$.Total maximum percentage error in density:$$\left(\frac{\Delta \rho}{\rho}\right) \times 100 = \left(\frac{\Delta m}{m} + \frac{2\Delta r}{r} + \frac{\Delta L}{L}\right) \times 100 = 1\% + 2\% + 1\% = 4\%$$Answer:The maximum percentage error in the measurement of density is $4\%$.Correct option: C. 4%