To calculate the volume of cylinder, a student is given a metre scale of least count 1 mm to measure its length and vernier callipers of least count 0.1 mm to measure its diameter. If its length and radius are 10 cm and 2 cm respectively then the percentage error in the calculated value of the volume of the cylinder will be

Options

A. `5%`
B. `4%`
C. `3%`
D. `2%`

Answer

d

Explanation

Volume of a cyclinder `V=pir^(2)L`
L.C. of metre scale = 0.1 cm and
L.C. of vernier = 0.01 cm
and `DeltaL=0.1cm, Deltar=0.01cm`
`therefore` Percentage error = `(DeltaV)/(V)xx100`
`=[2(Deltar)/(r)+(DeltaL)/(L)]xx100`
`=[2xx(0.01)/(2)+(0.01)/(10)]xx100`
`=[2xx(0.01)/(2)+(0.1)/(10)]xx100`
`=[(1)/(100)+(1)/(100)]xx100=2%`