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While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is $1 \mathrm{~mm}$ and circular scale reading is equal to $42$ divisions. Pitch of screw gauge is $1 \mathrm{~mm}$ and it has $100$ divisions on circular scale. The diameter of the wire is $\frac{x}{50} \mathrm{~mm}$. The value of $x$ is :
$142$
$71$
$42$
$21$
Solution
$\mathrm{MSR}=1 \mathrm{~mm}, \mathrm{CSR}=42, \text { pitch }=1 \mathrm{~mm}$
$\mathrm{LC}=\frac{\text { pitch }}{\text { No. of } \mathrm{CSD}}=\left(\frac{1}{100}\right)=0.01 \mathrm{~mm}$
$\text { Diameter }=\mathrm{MSR}+\mathrm{LC} \times \mathrm{CSD}$
$\text { Diameter }=1+(0.01) \times 42 \mathrm{~mm}$
$\text { Diameter }=1.42 \mathrm{~mm}=\frac{\mathrm{x}}{50}$
$\therefore \mathrm{x}=71$
