Consider the diameter of a spherical object being measured with the help of a Vernier callipers. Suppose its 10 Vernier Scale Divisions (V.S.D.) are equal to its 9 Main Scale Divisions (M.S.D.). The least division in the M.S. is 0.1 cm and the zero of V.S. is at x = 0.1 cm when the jaws of Vernier callipers are closed.
If the main scale reading for the diameter is M = 5 cm and the number of coinciding vernier division is 8, the measured
diameter after zero error correction, is
Correct Answer :
4.98 cm
Solution :
To find the corrected diameter of the spherical object, we will break down the calculation into systematic steps: finding the least count of the Vernier calipers, determining the zero error, calculating the observed reading, and applying the zero error correction.
Step 1: Calculate the Least Count (L.C.) of the Vernier calipers
We are given that:
10 Vernier Scale Divisions (V.S.D.) = 9 Main Scale Divisions (M.S.D.)
Therefore, 1 V.S.D. = 0.9 M.S.D.
The value of the smallest division on the Main Scale (1 M.S.D.) is given as:
The Least Count (L.C.) is defined as:
Step 2: Determine the Zero Error
When the jaws of the Vernier calipers are closed, the zero of the Vernier scale lies at:
Since the zero of the Vernier scale lies to the right of the main scale zero (a positive position), there is a positive zero error.
Step 3: Calculate the Observed Reading
The main scale reading (M) is given as 5 cm.
The coinciding Vernier division (n) is 8.
The observed reading is calculated as:
Step 4: Apply the Zero Error Correction
The measured diameter after correcting for the zero error is given by:
Thus, the measured diameter of the spherical object after zero error correction is 4.98 cm.
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