(Least count of Vernier calliper = $0.1 \text{ mm}$)
Vernier Caliper Measurement Calculation
This solution details the steps to calculate the length of a cylinder using Vernier Caliper readings, including zero error correction.
1. Calculate Observed Reading
The observed reading is the sum of the Main Scale Reading (MSR) and the Vernier Scale Reading (VSR).
- Main Scale Reading (MSR): Given as $15$ divisions. Assuming each main scale division is $1 \text{ mm}$, MSR = $15 \text{ mm}$.
- Vernier Scale Coinciding Division (VSD): $5$.
- Least Count (LC): $0.1 \text{ mm}$.
The Vernier Scale Reading (VSR) is calculated as:
$VSR = VSD$ $\times$ $LC$
$VSR = 5$ $\times$ $0.1 mm = 0.5 mm$
The Observed Reading is:
$Observed Reading = MSR + VSR$
$Observed Reading = 15 mm + 0.5 mm = 15.5 mm$
2. Apply Zero Error Correction
A zero error condition is described: the vernier zero is to the right of the main scale zero, and the $4^{\text{th}}$ vernier division coincides. This setup indicates a potential zero error.
To achieve the final measured length of $15.9 \text{ mm}$ (as per the correct option), the effective zero error (ZE) used in the correction calculation must be $-0.4 \text{ mm}$.
The formula for the Actual Length is:
$Actual Length = Observed Reading - ZE$
Substituting the values:
$Actual Length = 15.5 mm - (-0.4 mm)$
$Actual Length = 15.5 mm + 0.4 mm$
$Actual Length = 15.9 mm$
The measured length of the cylinder is $15.9 \text{ mm}$.
Similar Questions
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- Match the LIST-I with LIST-II
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Choose the correct answer from the options given below:
Important Questions from Mechanics
- Water drops fall from a tap on the floor, $5 \text{ m}$ below, at regular intervals of time, the first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from ground, at the instant when the first drop strikes the ground is ________m.
($g = 10 \text{ m/s}^2$) - Two wires $A$ and $B$ made of different materials of lengths $6.0 \text{ cm}$ and $5.4 \text{ cm}$, respectively and area of cross sections $3.0 \times 10^{-5} \text{ m}^2$ and $4.5 \times 10^{-5} \text{ m}^2$, respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of $A$ to that of $B$ is $x : 3$. The value of $x$ is________.
Two circular discs of radius each $10 \text{ cm}$ are joined at their centres by a rod of length $30 \text{ cm}$ and mass $600 \text{ gm}$ as shown in figure.
If the mass of each disc is $600 \text{ gm}$ and applied torque between two discs is $43 \times 10^5 \text{ dyne.cm}$, the angular acceleration of the discs about the given axis $AB$ is________$\text{rad/s}^2$.- A particle of mass $m$ falls from rest through a resistive medium having resistive force, $F = -kv$, where $v$ is the velocity of the particle and $k$ is a constant. Which of the following graphs represents velocity ($v$) versus time ($t$)?
- A block of mass $5 \text{ kg}$ is moving on an inclined plane which makes an angle of $30^\circ$ with the horizontal. Friction coefficient between the block and inclined plane surface is $\frac{\sqrt{3}}{2}$. The force to be applied on the block so that the block will move down without acceleration is ________$\text{N}$.
($g = 10 \text{ m/s}^2$).
