Chapter – 1
General Physics
Syllabus
General Units and dimensions, dimensional analysis; least count, significant figures; Methods of measurement and error analysis for physical quantities pertaining to the following experiments: Experiments based on using Vernier calipers and screw gauge (micrometer), Determination of g using simple pendulum, Young’s modulus – elasticity of the material Surface tension of water by capillary rise and effect of detergents. Specific heat of a liquid using calorimeter, focal length of a concave mirror and a convex lens using u-v method, Speed of sound using resonance column, Verification of Ohm’s law using voltmeter and ammeter, and specific resistance of the material of a wire using meter bridge and post office box.
Notes: Topics before experiments can be seen in JEE Mains Physics and Measurement.
Vernier calipers
It is a length measuring device used to measure accurately up to 1/10th of milimetre.
Construction:
(i) Scales: It comprises of two scales, viz., main scale M and vernier scale V which is called auxiliary scale. The main scale is fixed but vernier scale is movable. The divisions of vernier scale are usually a little smaller in size than the smallest division on the main scale.
(ii) Jaws: It has two jaws, one attached with the main scale and other with the vernier scale. The purpose of jaws are to grip the object between them.
(iii) Strips: Vernier has a strip, which slide along with vernier scale, over the main scale. This strip is used to measure the depth of hollow object.
Theory:
Vernier constant (V.C.): The difference between the values of one main scale division and one vernier scale division is known as Vernier constant (V.C.) or the Least count (L.C.).
Least Count is the smallest distance that can be accurately measured with the vernier scale.
Let ‘n’ vernier scale divisions (V.S.D.) coincide with (n-1) main scale divisions (M.S.D.). Then
$$n\ V.S.D.=(n-1)\ M.S.D.$$ $$1\ V.S.D.=\frac{n-1}{n}\ M.S.D.$$
\(V.C.\ or\ L.C.\ =\ 1\ M.S.D.\ -\ 1\ V.S.D.\)
\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \ 1\ M.S.D.\ -\ \frac{n-1}{n}\ M.S.D.\)
\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \ \frac{1}{n}\ M.S.D.\)
Therefore, \( L.C.\ =\ \frac{Smallest\ division\ on\ main\ scale}{Number\ of\ divisions\ on\ vernier\ scale}\)
In the ordinary vernier calipers one main scale division be 1 mm and 10 vernier divisions coincide with 9 main scale divisions.
\(\ \ \ \ \ \ \ \ 1\ V.S.D.\ =\ \frac{9}{10}\ M.S.D.\ =\ 0.9\ mm\)
Therefore, \( L.C.\ =\ 1\ M.S.D.\ -\ 1\ V.S.D.\)
\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \ 1\ mm\ -\ 0.9\ mm\)
\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \ 0.1\ mm\ =\ 0.01\ cm\)
Positive and Negative error:
(i) Positive error: If zero of vernier scale lies to the right of the main scale the zero error is positive error (when jaw J1 and J2 are in contact).
Positive zero error = + [N + m x L.C.]
Where, N = main scale reading on the left of zero of vernier scale.
m = vernier scale division which coincides with any main scale division.
For example, from above figure, we have
N = 0.00 cm, m = 6 and L.C. = 0.01 cm, therefore,
Positive zero error = + [0 + 6 x 0.01] cm = 0.06 cm
(ii) Negative error: If zero of vernier scale lies to the left of the main scale the zero error is negative error (when jaw J1 and J2 are in contact).
Negative zero error = – [N + m x L.C.]
From above figure, we have
N = 0.00 cm, m = 6 and L.C. = 0.01 cm, therefore,
Negative zero error = – [0 + 6 x 0.01] cm = – 0.06 cm
(i) No zero error: When the zero of the vernier scale coincides with the zero of the main scale, there is no zero error.
(ii) Zero correction = – zero error
Reading a vernier callipers
If we have to measure a length AB, the end A is coincide with the zero of main scale, suppose the end B lies between 1.1 cm and 1.2 cm on the main scale. Then
1.1 cm < AB < 1.2 cm