Question

A screw gauge having $100$ equal divisions and a pitch length of $1\text{mm}$ is used to measure the diameter of a wire of length $5.6\text{cm}$. The main scale reading is $1\text{mm}$ and ${47}^{\text{th}}$ circular division coincides with the main scale. The curved surface area of wire (in ${\text{cm}}^2$) to appropriate significant figures is

• A. $1.60$
• B. $3.20$
• C. $1.25$
• D. $2.6$

Answer 1

The correct option is D $2.6$

Least count $\left(LC\right)=$ $1\text{mm}/100=0.01\text{mm}$
Diameter $=MSR+CSR\times LC$
$\Rightarrow d=1+47\times 0.01=1.47\text{mm}$
Surface area,
$S=\pi dl$
$\Rightarrow S=\frac{22}{7}\times 1.47\times 56$
$\Rightarrow S=258.72{\text{mm}}^2=2.5872{\text{cm}}^2$
$\Rightarrow S=2.6{\text{cm}}^2$