Question

Volume of a cylindrical wire is measured with the help of a simple scale with 10 divisions per centimeter to measure length and a screw gauge with 100 divisions on circular scale with a pitch of 1 mm to measure the diameter. If length is 20 cm and diameter is 1 mm, then percentage error in volume is

• A. 5%
• B. 2.5%
• C. 10%
• D. 20%

Answer 1

The correct option is B 2.5%

Given,

Screw gauge has 100 divisions

Pitch = 1 mm

Length = 20 cm and diameter is 1 mm

Volume is given as

$V=\pi \frac{D^2}{4}L$

Now we can write and put the respective values
$V=\frac{\pi D^2}{4}L\Rightarrow \frac{\Delta V}{V}=\frac{2\Delta D}{D}+\frac{\Delta L}{L}=2\times \frac{1}{100}\times \frac{1}{1}+\frac{0.1}{20}$
$\frac{\Delta V}{V}\times 100=2\%+0.5\%=2.5\%$

Hence the percentage error is 2.5 %