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  • It is found that the zero of the Vernier scale lies between  and <img alt="5.20

It is found that the zero of the Vernier scale lies between 5.15 \mathrm{~cm} and 5.20 \mathrm{~cm} of the main scale. The Vernier scale has 50 divisions equivalent to 2.55 \mathrm{~cm}. The 22nd division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is:

Option: 1

5.212 \mathrm{~cm}


Option: 2

5.224 \mathrm{~cm}


Option: 3

5.236 \mathrm{~cm}


Option: 4

5.216 \mathrm{~cm}


Answers (1)

best_answer

Step 1: Determine the main scale reading range: The zero of the Vernier scale lies between 5.15 \mathrm{~cm} and 5.20 \mathrm{~cm}. This means the main scale reading (MSR) can be any value between these two extremes.

Step 2: Calculate the value of one main scale division: Since the main scale reading range is from 5.15 \mathrm{~cm} to 5.20 \mathrm{~cm}, the difference is 0.05 \mathrm{~cm}. Divide this difference by the number of divisions on the main scale to get the value of one main scale division.

Value of one main scale division=0.05 \mathrm{~cm}

Step 3: Calculate the value of one Vernier scale division: Given that the Vernier scale has 50 divisions equivalent to 2.35 \mathrm{~cm}, divide the total length of the Vernier scale by the number of divisions to get the value of one Vernier scale division. 

$$
\text { Value of one Vernier scale division }=\frac{2.35 \mathrm{~cm}}{50}=0.047 \mathrm{~cm}
$$

Step 4: Calculate the least count (LC): The least count is the difference between the values of one main scale division and one Vernier scale division.

Least Count $(\mathrm{LC})=$ Value of one main scale division - Value of one Vernier scale division $=0.05 \mathrm{~cm}-0.04$

Step 5: Calculate the true main scale reading: Since the 22nd division of the Vernier scale coincides with a main scale division, we can add 22 main scale divisions to the minimum main scale reading to find the true main scale reading.

True Main Scale Reading =5.15 \mathrm{~cm}+(22 \times$ Value of one main scale division $)=5.15 \mathrm{~cm}+(22 \times 0.003 \mathrm{~cm})=5

Step 6: Calculate the diameter of the cylinder: Since the cylinder's diameter is twice its radius, we can directly use the true main scale reading as the diameter.

Diameter of the Cylinder =5.172 \mathrm{~cm}
 

So, the diameter of the cylinder is approximately 5.172 \mathrm{~cm}.

 

Posted by

sudhir.kumar

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