ERRORS
The result of every measurement by any measuring instrument contains some uncertainty this uncertainty is called errors. The errors in a measurement is equal to the difference between the true value and the measured value of any quantity.
Errors = True value – Measured value
Absolute Errors:- the several values obtained in an experiment measured are a1, a2, a3….an the arthmetic mean of these values will be
Now error in first measurement = Da1 = amean –a1
Similarly in second measurement = Da2 = amean –a2 and so on
Relative error:Relative error=∆ameanamean
Combination of errors (maximum possible error) Addition or subtraction
Product or multiplication
Let
Division
(4) Powers
Let C = anbm
CONCEPT WITH EXAMPLES
Role of constants
The radius of sphere is measured to be (2.1 ± 0.5) cm and is surface area with error limits.
Solution:
Surface area = A = 4pr2
Now% error
= 47.62 %
Other way
= 4 p r2
= 55.4 cm2
= 26.4 cm2
Now (A ± DA)
= (55.4±26.4)
FINDING QUANTITY
Percentage error in determining of acceleration of gravity with the help of simple Pendulum time period . Given error in length of pendulum 4% while in The time period it is 2% then percentage error in g = ?
Solution
LEAST COUNT AND DIFFERENT UNITS
If a particle of mass m = 25.0 Kg is moving in a circular path of radius r = 50.00 cm with constant speed of v = 10.0 Km/hr them find error in force required by particle.
Now Given
m = 25.0 Kg
= L.c. = 0.1
V = 10.0 Km/h
= L.c = 0.1
DV = 0.1, V = 10
R = 50.00 cm
Dr = 0.001, r = 50cm
NOTE: never change units in error.
Least count
25.00 – L.c = 0.01
16.50 – 50 –L.c = 0.01
76.03 – 03 –L.c = 0.01
15.0002 –L.c = 0.0001
17.030 – L.c = 0.01
Solution:
= 1.21 x 2= 2.42% Ans.
UNIQUE CONCEPT
Calculate focal length of a spherical Mirror from the following observations Object distance u = (50.1 ± 0.5) cm. and image distance v = (20.1 ± 0.2) cm.
= 14.3 cm
Now
± 0.4 cm
Note: Similar case in resistance connected in parallel combinations
SIGNIFICANT FIGURES
The number of significant figures of a numerical quantity is the number of reliably known digits it contains:
Rules:
1. Zeros at the beginning of a number are not significant.
Ex. 0.0523 – there S.f. (5, 2, 3)
2. Zeros within a number are significant.
Ex: 2056 –Four S.f. (2, 0, 5, 6)
3. Zeros at the end of a number after decimal points are significant.
Ex. 3702.0 –five S.f. (3, 7, 0, 2, 0)