Q: The length of a cylinder is measured with a meter rod having least count 0.1 cm. its diameter is measured with vernier calipers having least count 0.01 cm. given the length is 5.0 cm and radius is 2.00 cm. the percentage error in the calculated value of volume will be

(a) 2 %

(b) 1 %

(c) 3 %

(d) 4%

Ans: (c)

Solution: $\displaystyle V = \pi r^2 l $

$\displaystyle \frac{\delta V}{V} \times 100 = 2\frac{\delta r}{r} \times 100 + \frac{\delta l}{l} \times 100 $

$\displaystyle \frac{\delta V}{V} \times 100 = 2 \times \frac{0.01}{2} \times 100 + \frac{0.1}{5} \times 100 $

$\displaystyle \frac{\delta V}{V} \times 100 = 1 + 2 $

= 3 %