Units Dimensions And Measurements

To find the vernier constant of a Vernier caliper, we first consider the definition of the vernier constant: it is the smallest measurement that can be calculated using a Vernier caliper and is equal to the least count. In the given problem, it is stated that $N%2B1$ divisions of the Vernier scale coincide with $N$ divisions of the main scale.

The given information can be expressed as:

1 Main Scale Division (MSD) = 0.1 mm

Therefore, $N$ divisions on the main scale equal:

$N%20%5Ctimes%200.1%20%5C%2C%20%5Ctext%7Bmm%7D%20%3D%200.1N%20%5C%2C%20%5Ctext%7Bmm%7D$

The Vernier scale is set such that $N%2B1$ Vernier scale divisions coincide with $N$ main scale divisions, giving each Vernier scale division:

$%5Cfrac%7B0.1N%7D%7BN%2B1%7D%20%5C%2C%20%5Ctext%7Bmm%7D$

The Vernier constant (VC) is the difference between one main scale division and one Vernier scale division, which is:

$VC%20%3D%20%5Ctext%7BMSD%7D%20-%20%5Ctext%7BVSD%7D%20%3D%200.1%20%5C%2C%20%5Ctext%7Bmm%7D%20-%20%5Cfrac%7B0.1N%7D%7BN%2B1%7D%20%5C%2C%20%5Ctext%7Bmm%7D$

$VC%20%3D%20%5Cfrac%7B0.1(N%2B1)%20-%200.1N%7D%7BN%2B1%7D$

$VC%20%3D%20%5Cfrac%7B0.1%7D%7BN%2B1%7D%20%5C%2C%20%5Ctext%7Bmm%7D$

Since we need the vernier constant in centimeters, convert mm to cm (1 mm = 0.1 cm):

$VC%20%3D%20%5Cfrac%7B0.1%20%5Ctimes%200.1%7D%7BN%2B1%7D%20%5C%2C%20%5Ctext%7Bcm%7D$

$VC%20%3D%20%5Cfrac%7B0.01%7D%7BN%2B1%7D%20%5C%2C%20%5Ctext%7Bcm%7D$

Expressed as a fraction, this becomes:

$%5Cfrac%7B1%7D%7B100(N%2B1)%7D%20%5C%2C%20%5Ctext%7Bcm%7D$

Thus, the vernier constant in centimeters is $%5Cfrac%7B1%7D%7B100(N%2B1)%7D$ .

High-Yield Trend

Chapter Questions
4 MCQs

Official Solution

Official Solution

Official Solution

Official Solution

Units Dimensions And Measurements

High-Yield Trend

Chapter Questions 4 MCQs

Official Solution

Official Solution

Official Solution

Official Solution

Chapter Questions
4 MCQs