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(a) Youare given a thread and a metre scale. How will you estimate the diameter of the thread?
(b) A screw gauge has a pitch of $1.0 \mathrm{~mm}$ and 200 divisions on the circular scale. Do you think it is possible to increase the accuracy of the screw gauge arbitrarily by increasing the number of divisions on the circular scale?
(c) The mean diameter of a thin brass rod is to be measured by Vernier callipers. Why is a set of 100 measurements of the diameter expected to yield a more reliable estimate than a set of 5 measurements only?
(a) Youare given a thread and a metre scale. How will you estimate the diameter of the thread?
(b) A screw gauge has a pitch of $1.0 \mathrm{~mm}$ and 200 divisions on the circular scale. Do you think it is possible to increase the accuracy of the screw gauge arbitrarily by increasing the number of divisions on the circular scale?
(c) The mean diameter of a thin brass rod is to be measured by Vernier callipers. Why is a set of 100 measurements of the diameter expected to yield a more reliable estimate than a set of 5 measurements only?
Solution:
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Verified Answer
(a) Meter scale can not measure small diameter of thread. No. of turns of the thread to be wound to get turns closely one another.
Let $l$ - measured length of windings on the scale which contains $n$ no. of turns.
$\therefore$ Diameter of thread $=\frac{l}{n}$.
(b) Least count $=\frac{\text { pitch }}{\text { no. of division in circular scale }}$ i.e. least count decreases when no. of division on the circular scale increases. Thereby accuracy would increase. but practically, it is impossible to take precise reading due to low resolution of human eye.
(c) Large no. of observations (say 100) gives more reliable result, because probability of making random error in positive side of a physical quantity would be same that of in negative side. Therefore, when no. of observations is large random errors would cancel each other and hence result would be reliable.
Let $l$ - measured length of windings on the scale which contains $n$ no. of turns.
$\therefore$ Diameter of thread $=\frac{l}{n}$.
(b) Least count $=\frac{\text { pitch }}{\text { no. of division in circular scale }}$ i.e. least count decreases when no. of division on the circular scale increases. Thereby accuracy would increase. but practically, it is impossible to take precise reading due to low resolution of human eye.
(c) Large no. of observations (say 100) gives more reliable result, because probability of making random error in positive side of a physical quantity would be same that of in negative side. Therefore, when no. of observations is large random errors would cancel each other and hence result would be reliable.
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