The vernier constant of a travelling microscope is 0.001 cm. If 49 main scale divisions coincide with 50 vernier scale divisions, then the value of 1 main scale division is:

A. 0.01mm

B. 0.02cm

C. 0.05cm

D. 0.0005cm

To determine the value of one main scale division (MSD) in a travelling microscope, we can use the relationship between the main scale and the vernier scale. Given that the vernier constant is 0.001 cm and that 49 main scale divisions coincide with 50 vernier scale divisions, we can set up our calculations accordingly.

Understanding the Relationship

The vernier constant (VC) is defined as the difference between one main scale division (MSD) and one vernier scale division (VSD). In this case, we know:

• Vernier Constant (VC) = 0.001 cm
• 49 MSD = 50 VSD

Calculating the Value of One Main Scale Division

From the information provided, we can express the relationship mathematically. Let’s denote the value of one main scale division as x cm. Therefore, the total length represented by 49 MSDs is:

49x = 50VSD

Now, we can express the value of the vernier scale division in terms of the vernier constant:

VSD = MSD - VC

Substituting the value of VC, we have:

VSD = x - 0.001

Setting Up the Equation

Now, substituting this back into our earlier equation:

49x = 50(x - 0.001)

Solving for x

Expanding the equation gives us:

49x = 50x - 0.05

Rearranging the terms leads to:

50x - 49x = 0.05

x = 0.05 cm

Final Answer

Thus, the value of one main scale division is 0.05 cm. Looking at the options provided:

• A. 0.01 mm
• B. 0.02 cm
• C. 0.05 cm
• D. 0.0005 cm

The correct answer is C. 0.05 cm.

Summary of the Calculation

In summary, by understanding the relationship between the main scale and the vernier scale, and using the vernier constant, we were able to derive that one main scale division equals 0.05 cm. This method can be applied to similar problems involving travelling microscopes or other measuring instruments that utilize a vernier scale.