JEE Physics 2023 Question with Solution

Step-by-step solution

Common mistakes

• Using $\frac{\Delta \rho}{\rho} = \frac{\Delta m}{m} + \frac{\Delta \ell}{\ell} + \frac{\Delta r}{r}$ and forgetting that $r$ is squared in the density formula. This is wrong because the power of $r$ contributes a factor of $2$ in relative error. Use $2\frac{\Delta r}{r}$ instead.

• Subtracting errors because $r$ and $\ell$ are in the denominator. This is wrong for maximum error calculation, where relative errors are added irrespective of numerator or denominator. Add all fractional errors.

• Converting the final fractional error $0.04$ directly into the answer without multiplying by $100$. This is wrong because the options are in percentage. Convert to percentage to get $4\%$.