The length of a uniform rod is 100.0 ,cm and | vedclass

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(A) The volume of a cylinder is given by $V = \pi r^2 l$.The relative error in volume is given by $\frac{\Delta V}{V} = 2 \frac{\Delta r}{r} + \frac{\

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(A) The volume of a cylinder is given by $V = \pi r^2 l$.The relative error in volume is given by $\frac{\Delta V}{V} = 2 \frac{\Delta r}{r} + \frac{\Delta l}{l}$.Given values:Length $l = 100.0 \,cm = 1000 \,mm$,$\Delta l = 1 \,mm$.Radius $r = 1.00 \,cm = 10.0 \,mm$,$\Delta r = 0.1 \,mm$.Substituting these values into the error formula:$\frac{\Delta V}{V} = 2 	imes \left( \frac{0.1}{10.0} ight) + \left( \frac{1}{1000} ight)$.$\frac{\Delta V}{V} = 2 	imes (0.01) + 0.001 = 0.02 + 0.001 = 0.021$.The percentage error is $\frac{\Delta V}{V} 	imes 100 = 0.021 	imes 100 = 2.1 \%$.Therefore,the correct option is $A$.

The length of a uniform rod is $100.0 \,cm$ and radius is $1.00 \,cm$. If length is measured with a meter rod having least count $1 \,mm$ and radius is measured with vernier callipers having least count $0.1 \,mm$,the percentage error in calculated volume of cylinder is ............. $\%$

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