physical quantities Flashcards
physical quantities
a measurable quantity in terms of which the laws of physics are expressed
unit
a standard chosen quantity in term of which a physical quantity is measured
dimension
power to be raised on a fundamental quantities like mass(m) , length(l) ,and time (T) involved in derived physical quantity
dimensional formula
the symbolic representation of dimension of physical formula in the term of m, l ,t inside larger bracket
dimension equation
the dimensional formula written in the form of equation
uses of dimensional formula
- to find the dimension of constant
- to check the correctness of the equation
- to convert one system unit to another
- to derive the formula
principle of homogeneity
for a equation to be correct, the dimension of each term of lhs must be equal to dimension of each term on rhs
limitation of dimensional formula
- it cant be said whether a physical quantity is a scalar or a vector
- the dimensional method cant be used to derived relations other than product of power function
- there are many physical quantities which have the same dimensional formula
- the relationship between more then three quantities involved in a physical phenomenon cant be derived by dimensional method
error
degree of uncertainty in a measurement from real or standard value
real error
real value - ovserved value
relative error
real error/real value
percentage error
relative error*100%
accuracy
measure of the difference of the experimental value and the true value(closeness betn values)
accuracy = mean value - true value
precision
difference between a measured value and the arithmetic mean value for a series of measurement(less the value more the precision)
precision = individual value - arithmetic value
significant figure
the no/digits that plays significant role in a number
notes
- the dimension is only a way to write a unit of a physical quantity. quantity either constant or variable may or may not have dimension.
- if dimensional formula is given, the physical quantity may or may not be unique .i.e. different physical quantities may have the same dimensions
- if a quantity ha dimensional formal , it must have a unit but the converse may or may not be true
- a quantity which is the ratio of two same quantities is dimensionless
is dimensional correct equation necessarily physically correct?
no. an equation dimensional correct needs not to be physically correct but the converse must be true
s=2ut+at^2(dimensional correct but physically incorrect)
is dimensional correct equation necessarily physically correct?
no. an equation dimensional correct needs not to be physically correct but the converse must be true
s=2ut+at^2(dimensional correct but physically incorrect)
the diameter of a steel rod is given s 56.47+_0.02 mm .what does it means?
0.02 represents uncertainty in measurement
diameter lies betn 56.45 and 56.49 mm. thus the above measurement is unlikely to be less than 56.45 mm or greater than 56.49 mm.
rules of significant role
25400(3) >without unit 25400 m(5) with unit 6540025 (7)sandwiched betn nos 0.65400025(8)in decimal 0.000645005(6)in decimal 1.00654005(9)sandwiched betn nos 2.268+2.5=2768 6.25*2.55/1.6=9.9
to find the dimension of constant
a.first, put the constant in the rhs place if it is in product form
b.compare the dimension of each element and the comparison can help to find the dimension of constant
c.if it is dimensionless constant just solve the element inside it in dimensional form and find the dimension of constant
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to check the correctness of the equation
a. rewrite the eqn in dimensional equation form
b. check whether the dimension of lhs = dimension of rhs
to convert one system unit to another
n2=n1 [m2/m1] ^ a * [l2/l1] ^ b * [t2/t1] ^ c
where a, b, and c are the dimension, m, l and t are mass, length and time in respective system and n1 is the magnitude
to derive the formula
a. depends on something and is related to it
b. combine them
c. write the dimension and solve the eqn
d. put the value in formed equation and derive the formula
