Question

The least count of the main scale of a vernier callipers is $1\text{mm}$. Its vernier scale is divided into $10$ divisions and coincide with $9$ divisions of the main scale. When jaws are touching each other, the $7^{\text{th}}$ division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale between $3.1\text{cm}$ and $3.2\text{cm}$ and $4^{\text{th}}\text{VSD}$ coincides with a main scale division. The length of the cylinder is $(\text{VSD}$ is vernier scale division$)$

• A. $2.99\text{cm}$
• B. $3.21\text{cm}$
• C. $3.21\text{cm}$
• D. $3.07\text{cm}$

Answer 1

The correct option is D $3.07\text{cm}$

Given that,
$\text{L.C.}$ of main scale $=1\text{mm \&}$
$9\text{MSD}=10\text{VSD}$

$\therefore 1\text{VSD}=0.9\text{MSD}=0.9\text{mm}$

So, the $\text{L.C.}$ of vernier scale will be

$\text{L.C.= 1MSD – 1VSD}$

$\text{L.C.= 1 MSD - 0.9 MSD = 0.1 MSD}$

$\therefore \text{L.C. = 0.1 mm = 0.01 cm}$

Now, zero error will be,

$\text{Zero error}=0+(7\times \text{L.C.})=0.07\text{cm}$

So, the reading of vernier callipers will be,

$=(3.1\text{cm}+(4\times \text{L.C.})–\text{Zero error}$

$=\text{3.1 cm + 0.04 cm – 0.07 cm}$

$=3.07\text{cm}$

Hence, option $\left(\text{B}\right)$ is correct.