Which of the following instruments has minimum leastcount?a)A vernier ...
(a) Least count of vernier callipers
(∵ 1MSD = 1mm)
(b) Least count of screw gauge
(c) Least count of spherometer
= 0.0001cm
(d) Wavelength of light, λ = 10
−5 cm = 0.00001cm
Clearly the optical instrument is the most precise.
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Which of the following instruments has minimum leastcount?a)A vernier ...
Explanation:
To determine the instrument with the minimum least count, we need to compare the least counts of each instrument and choose the one with the smallest value.
Least count of an instrument:
The least count of an instrument is the smallest value that can be measured with that instrument. It determines the precision or accuracy of the instrument.
A) Vernier Calipers:
The least count of a vernier caliper is given by the formula:
Least Count = (1 Main Scale Division) - (1 Vernier Scale Division)
In this case, the number of divisions on the main scale is 19 and the number of divisions on the vernier scale is 20. Therefore, the least count of the vernier calipers is:
Least Count = 1 mm / (19 - 20) = 1 mm
B) Screw Gauge:
The least count of a screw gauge is given by the formula:
Least Count = (Pitch) / (Number of Circular Scale Divisions)
In this case, the pitch is 1 mm and the number of divisions on the circular scale is 100. Therefore, the least count of the screw gauge is:
Least Count = 1 mm / 100 = 0.01 mm
C) Spherometer:
The least count of a spherometer is given by the formula:
Least Count = (Pitch) / (Number of Circular Scale Divisions)
In this case, the pitch is 0.1 mm and the number of divisions on the circular scale is 100. Therefore, the least count of the spherometer is:
Least Count = 0.1 mm / 100 = 0.001 mm
D) Optical Instrument:
An optical instrument that can measure length to within a wavelength of light has the smallest possible least count. The wavelength of light is on the order of nanometers (10^-9 meters), which is smaller than the least counts of the other instruments.
Therefore, the optical instrument has the minimum least count.
Conclusion:
Among the given options, the instrument with the minimum least count is the optical instrument that can measure length to within a wavelength of light.
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