Answer the following : (a)You are 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 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)
First, wrap the thread on a cylindrical coil by keeping the turns of the thread in such a way that they are touching each other side by side. After completion of the wrapping of thread on the coil, measure the length of the coil up to the wrapped portion.
Let n be the number of turns over the coil and l be the length of the coil up-to wrapped portion.
The diameter of the thread can be estimate by,
d = length of the wrapped coil number of turns = l n
(b)
Given, the pitch of the screw gauge is 1.0 mm and the number of division on the circular scale is 200.
The lower the value of the least count of an instrument, the more precise it is.
The least count of the screw gauge is given as,
Least count = pitch Number of division
From the above relation it can be said that with the increase in the number of division, the value of least count decreases. So the accuracy of the screw gauge also increases. But there is a certain limit up-to which the number of division increases, after which it becomes difficult to increase the number of division on the circular scale. So, it is possible to increase the accuracy of the screw gauge arbitrarily by increasing the number of division on the circular scale.
(c)
Reliable refers to the degree of accuracy in the measurement. Reliability increases with increase in the number of the measurements. It is because the chances of random error in the large number of measurements are very less as compared to the chances of random error in small number of observation. So the set of 100 measurements of a diameter is more reliable than a set of 5 measurements.
(a)
First, wrap the thread on a cylindrical coil by keeping the turns of the thread in such a way that they are touching each other side by side. After completion of the wrapping of thread on the coil, measure the length of the coil up to the wrapped portion.
Let n be the number of turns over the coil and l be the length of the coil up-to wrapped portion.
The diameter of the thread can be estimate by,
(b)
Given, the pitch of the screw gauge is
The lower the value of the least count of an instrument, the more precise it is.
The least count of the screw gauge is given as,
From the above relation it can be said that with the increase in the number of division, the value of least count decreases. So the accuracy of the screw gauge also increases. But there is a certain limit up-to which the number of division increases, after which it becomes difficult to increase the number of division on the circular scale. So, it is possible to increase the accuracy of the screw gauge arbitrarily by increasing the number of division on the circular scale.
(c)
Reliable refers to the degree of accuracy in the measurement. Reliability increases with increase in the number of the measurements. It is because the chances of random error in the large number of measurements are very less as compared to the chances of random error in small number of observation. So the set of 100 measurements of a diameter is more reliable than a set of 5 measurements.
