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Units and measurement
A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can be expressed as a multiple of the unit of measurement. For example, a length is a physical quantity. The metre is a unit of length that represents a definite predetermined length. When we say 10 metres (or 10 m), we actually mean 10 times the definite predetermined length called "metre".
Measurement is a process of determining how large or small a physical quantity is as compared to a basic reference quantity of the same kind.
But not all quantities require a unit of their own. Using physical laws, units of quantities can be expressed as combinations of units of other quantities. Thus only a small set of units is required.
Base and derived units
These units are taken as the base units and the other units are derived units. Thus base units are the units of the quantities which are independent of other quantities and they are the units of length, mass, time, electric current, temperature, luminous intensity and the amount of substance. Derived units are the units of the quantities which are derived from the base quantities and some of the derived units are the units of speed, work, acceleration, energy, pressure etcDifference between mass and weight
The mass, strictly the inertial mass, relates the acceleration of a body to the applied force via Newton's law:
F=ma
The weight is the force a body exerts when it is in a gravitational field. The weight depends on the gravitational field. For example the weight of a 1kg mass at the Earth's surface is 9.81 Newtons, while at the surface of Mars it's about 3.5 Newtons.
This is possibly a bit too much info: if so ignore this last paragraph. Although weight specifically means the force exerted in a gravitational field, Einstein told us that sitting stationary in a gravitational field is equivalent to being accelerated in the absence of gravity. The inertial mass defined using Newton's laws is the same as the gravitational mass defined by the force a body exerts in a gravitational field.
Principle of homogeneity
The principle of homogeneity states that the dimensions of each the terms of a dimensional equation on both sides are the same. Using this principle the given equation will have same dimension on both sides.
Below important dimensional formula listed with correctness of physical equation
Accuracy
It refers to the closeness of a measurement to the true value of the physical quantity.
It indicates the relative freedom from errors. As we reduce the errors, the measurement becomes more accurate .
Precision
It refers to the resolution or the limit to which the quantity is measured .
It is determined by the least count of the measuring instrument. The smaller the least count, greater is the precision.
Errors in measurement
Every measurement is done with the help of some instrument. While making the measurement, some uncertainty gets occurred
Error
The difference between the true value and the measured value of the quantity is know as error.
Different types of errors
- Constant error
The errors which affect each observation by the same amount .
- Systematic error
The error which tend to occur in one direction, either positive or negative.
- Random errors
The errors which occur irregularly and at random, in magnitude and direction .
- Least count error
The smallest division on the scale of the measuring instrument.
- Gross error or mistakes
These errors are due to either carelessness of the person or due to improper adjustment of the apparatus.
Absolute error
The magnitude of the difference between the true value of the quantity measured and the individual measured value.
Relative error
The ratio of the mean absolute error to the true value of measured quantity.
Percentage error
The relative error expressed in percent is be percentage error.
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