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Experimental Physics

JEE Main · Physics · Experimental Physics

A vernier caliper has a main scale with 2 divisions per millimeter....

A vernier caliper has a main scale with 22 divisions per millimeter. It is given that 5050 vernier scale divisions coincide with 4949 main scale divisions. When measuring the diameter of a spherical body, the zero of the vernier scale lies just after the 12.5 mm12.5 \text{ mm} mark on the main scale, and the 24th24^{\text{th}} vernier division coincides with a main scale division. If the instrument has a positive zero error of 0.04 mm0.04 \text{ mm}, the true diameter of the body is :

Options

  1. A12.70 mm12.70 \text{ mm}
  2. B12.78 mm12.78 \text{ mm}
  3. C12.94 mm12.94 \text{ mm}
  4. D12.74 mm12.74 \text{ mm}

Correct answer

A. 12.70 mm12.70 \text{ mm}

Step-by-step solution

The main scale has 22 divisions per millimeter.
Length of one main scale division (1 MSD1 \text{ MSD}) =1 mm2=0.5 mm= \dfrac{1 \text{ mm}}{2} = 0.5 \text{ mm}

Given that 50 VSD=49 MSD50 \text{ VSD} = 49 \text{ MSD}
⇒1 VSD=4950 MSD\Rightarrow 1 \text{ VSD} = \dfrac{49}{50} \text{ MSD}

The least count (LC) of the vernier caliper is:
LC=1 MSD−1 VSD\text{LC} = 1 \text{ MSD} - 1 \text{ VSD}
LC=1 MSD−4950 MSD=150 MSD\text{LC} = 1 \text{ MSD} - \dfrac{49}{50} \text{ MSD} = \dfrac{1}{50} \text{ MSD}
LC=150×0.5 mm=0.01 mm\text{LC} = \dfrac{1}{50} \times 0.5 \text{ mm} = 0.01 \text{ mm}

The measured reading is calculated as:
Measured Reading=Main Scale Reading (MSR)+(Vernier Scale Reading (VSR)×LC)\text{Measured Reading} = \text{Main Scale Reading (MSR)} + (\text{Vernier Scale Reading (VSR)} \times \text{LC})
Measured Reading=12.5 mm+(24×0.01 mm)=12.5 mm+0.24 mm=12.74 mm\text{Measured Reading} = 12.5 \text{ mm} + (24 \times 0.01 \text{ mm}) = 12.5 \text{ mm} + 0.24 \text{ mm} = 12.74 \text{ mm}

The true reading is obtained by subtracting the zero error from the measured reading:
True Reading=Measured Reading−Zero Error\text{True Reading} = \text{Measured Reading} - \text{Zero Error}
True Reading=12.74 mm−(+0.04 mm)=12.70 mm\text{True Reading} = 12.74 \text{ mm} - (+0.04 \text{ mm}) = 12.70 \text{ mm}

Answer: 12.70 mm12.70 \text{ mm}
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