Question

The pitch of a screw gauge is $1m$ and there are $100$ divisions on the circular scale. While measuring the diameter of a wire, the linear scale reads $1mm$ and ${47}^{th}$ division on the circular scale coincides with the reference line. The length of the wire is $5.6cm$. Find the curved surface area (in $c{m}^2)$ of the wire in appropriate number of significant figures.

• A.
  $2.6$
• B. $4.8$
• C. $3.2$
• D.
  $1.3$

Answer 1

The correct option is A

$2.6$
Given, $\text{pitch}=1mm$
No of division on circular scale =$100$
So, least count of the screw gauge$L.C.=\frac{\text{pitch}}{\text{no of dividionson circular scale}}$
$L.C=\frac{1}{100}=0.01mm$

Given, main scale reading,
$MSR=1mm$
Circular scale reading, $VSR=47$
So, diameter of the wire or total reading of screw gauge $=MSR+(VSR\times LC)$
$d=1mm+(47\times 0.01)$
$d=1.47mm=0.147cm$

Given, length of the wire, $l=5.6cm$
So, the curved surface area of the wire,$A=2\pi rl=\pi dl$
$A=3.14\times 0.147\times 5.6$
$A=2.586c{m}^2$
Rounding off to two significant figure area will be $A=2.6c{m}^2$