MHTCET 15 Apr 2026 Shift 1 Paper

Concept:For a cylindrical rod, volume is $V = \pi r^2 l$. Since diameter is measured by the vernier callipers, express volume in terms of diameter: $V = \frac{\pi d^2 l}{4}$.Explanation:Given radius $r = 2.0\ \mathrm{cm}$, so diameter $d = 2r = 4.0\ \mathrm{cm}$.Diameter is measured by vernier callipers, so $\Delta d = 0.01\ \mathrm{cm}$.Length is measured by the meter scale, so $l = 5.0\ \mathrm{cm}$ and $\Delta l = 0.1\ \mathrm{cm}$.Using relative error for powers:$$\frac{\Delta V}{V} = 2\frac{\Delta d}{d} + \frac{\Delta l}{l}$$Percentage error in diameter term:$$2\frac{\Delta d}{d} \times 100 = 2 \times \frac{0.01}{4.0} \times 100 = 0.5\%$$Percentage error in length term:$$\frac{\Delta l}{l} \times 100 = \frac{0.1}{5.0} \times 100 = 2\%$$Total percentage error in volume:$$0.5\% + 2\% = 2.5\%$$Answer:Option B: $2.5\%$