Vernier Callipers Least Count Calculation
This section details the calculation for the least count (LC) of a vernier callipers based on the provided instrument specifications.
Given Information
- Number of Vernier Scale Divisions (VSD) = 50
- Number of Main Scale Divisions (MSD) equivalent to 50 VSD = 48
- Value of one Main Scale Division (1 MSD) = 0.05 mm
Least Count Formula
The least count represents the smallest measurement the instrument can accurately measure. It is calculated as the difference between the value of one main scale division and one vernier scale division.
$\text{Least Count (LC)} = 1 \text{ MSD} - 1 \text{ VSD}$
Calculation Steps
-
Relate Vernier Scale Divisions to Main Scale Divisions:
The problem states that 50 VSD are equal in length to 48 MSD.
From this, we find the value of 1 VSD in terms of MSD:
$1 \text{ VSD} = \frac{48}{50} \times 1 \text{ MSD}$
$1 \text{ VSD} = 0.96 \times 1 \text{ MSD}$
-
Calculate the value of 1 VSD in millimeters:
Substitute the value of 1 MSD (0.05 mm) into the equation from Step 1:
$1 \text{ VSD} = 0.96 \times 0.05 \text{ mm}$
$1 \text{ VSD} = 0.048 \text{ mm}$
-
Compute the Least Count (LC):
Apply the least count formula using the values of 1 MSD and 1 VSD:
$\text{LC} = 0.05 \text{ mm} - 0.048 \text{ mm}$
$\text{LC} = 0.002 \text{ mm}$
Result
Following the standard calculation method, the least count for the vernier callipers is determined to be 0.002 mm.
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Important Questions from Mechanics
- When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height h. If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by 1% each, then the height of the liquid in the tube will change by _________ %.
A uniform bar of length 12 cm and mass $20m$ lies on a smooth horizontal table. Two point masses $m$ and $2m$ are moving in opposite directions with same speed of $v$ and in the same plane as the bar, as shown in figure. These masses strike the bar simultaneously and get stuck to it. After collision the entire system is rotating with angular frequency $\omega$. The ratio of $v$ and $\omega$ is :
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- A spring of force constant 15 N/m is cut into two pieces. If the ratio of their length is 1:3, then the force constant of smaller piece is ______ N/m.
Match the LIST-I with LIST-II
List-I: List-II: A. Magnetic induction I. $[M L T^{-2} A^{-2}]$ B. Magnetic flux II. $[M L^2 T^{-2} A^{-2}]$ C. Magnetic permeability III. $[M L^0 T^{-2} A^{-1}]$ D. Self inductance IV. $[M L^2 T^{-2} A^{-1}]$ Choose the correct answer from the options given below:
