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A vernier caliper has 50 divisions which...

A vernier caliper has 50 divisions which are equivalent to 2.45 cm. Main scale reading of vernier caliper is found to be 4.15 cm. Markings on main scale are at 0.05 cm. The 24th division of vernier scale matches with one of the main scale divisions.

A

Least count `=0.001 cm`

B

Least count `=0.001 mm`

C

Final reading `=4.174 cm`

D

Final reading `=4.157 cm`

Text Solution

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The correct Answer is:
To solve the problem, we need to find the final reading of the vernier caliper using the given information. Here’s a step-by-step solution: ### Step 1: Calculate the Value of One Vernier Scale Division (VSD) We know that 50 divisions of the vernier scale are equivalent to 2.45 cm. To find the value of one division of the vernier scale, we use the formula: \[ \text{Value of 1 VSD} = \frac{2.45 \, \text{cm}}{50} \] Calculating this gives: \[ \text{Value of 1 VSD} = 0.049 \, \text{cm} \] ### Step 2: Identify the Main Scale Reading (MSR) The main scale reading (MSR) is given as 4.15 cm. ### Step 3: Calculate the Least Count (LC) The least count of the vernier caliper is defined as the difference between one main scale division (MSD) and one vernier scale division (VSD). Given that the markings on the main scale are at 0.05 cm, we have: \[ \text{Least Count (LC)} = \text{MSD} - \text{VSD} = 0.05 \, \text{cm} - 0.049 \, \text{cm} = 0.001 \, \text{cm} \] ### Step 4: Determine the Vernier Scale Reading (VSR) The problem states that the 24th division of the vernier scale matches with one of the main scale divisions. Therefore, the Vernier Scale Reading (VSR) is: \[ \text{VSR} = 24 \times \text{Value of 1 VSD} = 24 \times 0.049 \, \text{cm} = 1.176 \, \text{cm} \] ### Step 5: Calculate the Final Reading The final reading (FR) of the vernier caliper can be calculated using the formula: \[ \text{Final Reading (FR)} = \text{MSR} + \text{VSR} \] Substituting the values we have: \[ \text{FR} = 4.15 \, \text{cm} + 1.176 \, \text{cm} = 5.326 \, \text{cm} \] ### Step 6: Conclusion The final reading of the vernier caliper is: \[ \text{Final Reading} = 5.326 \, \text{cm} \]
To solve the problem, we need to find the final reading of the vernier caliper using the given information. Here’s a step-by-step solution: ### Step 1: Calculate the Value of One Vernier Scale Division (VSD) We know that 50 divisions of the vernier scale are equivalent to 2.45 cm. To find the value of one division of the vernier scale, we use the formula: \[ \text{Value of 1 VSD} = \frac{2.45 \, \text{cm}}{50} \] ...
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