Question

To determine the diameter of a rod a student wound a thread $5\mathrm{times}$ around the rod and measured the length of thread as $156\mathrm{mm}$on a meter scale. Using this value he calculated the diameter of the rod. If the actual diameter of the rod is $9.94\mathrm{mm}$what is the error that could result in the method followed by the student?$\mathrm{Take}\mathrm{\pi }=\frac{22}{7}$

• A. $+0.01mm$
• B. $-0.01mm$
• C. $+0.02mm$
• D. $-0.02mm$

Answer 1

The correct option is B

$-0.01\mathrm{mm}$

Step 1: Given data:

Actual Diameter of rod = 9.94 mm

Length of thread = 156 mm

The student wound the thread $5\mathrm{times}$around the rod.

which is equal to $5\mathrm{circumference}$ of the rod.

Step 2: Formula

$\because \mathrm{circumference}=\mathrm{\pi D}$

$$\begin{gathered} \therefore 5\mathrm{x}\left(\mathrm{circumference}\right)=156\mathrm{mm} \\ 5{\mathrm{\pi D}}_{measured}=156\mathrm{mm} \end{gathered}$$

$$\begin{gathered} \therefore {\mathrm{D}}_{\mathrm{m}}=\frac{156\times 7}{5\times 22} \\ =9.93\mathrm{mm} \end{gathered}$$

Hence the diameter of the rod found by the thread method is 9.93 mm.

$\because \mathrm{Actual}\mathrm{diameter}=9.94\mathrm{mm}$

$$\begin{gathered} \therefore \mathrm{Eorror}=({\mathrm{D}}_{\mathrm{actual}}-{\mathrm{D}}_{\mathrm{measured}}) \\ =9.94-9.93 \\ =0.01\mathrm{mm} \end{gathered}$$

since the measured value is less than actual

$\therefore \mathrm{error}=-0.01\mathrm{mm}$ .

The correct option is B.