Q. 14.7( 3 Votes )
Give an example of
(a) A physical quantity which has a unit but no dimensions
(b) A physical quantity which has neither unit nor dimensions
(c) A constant which has a unit
(d) A constant which has no unit
(a) A physical quantity which has a unit but no dimension is the angle.
Angle is dimensionless quantity, since:
[ ] is the notation used for dimension.
Hence, the angle is dimensionless quantity.
SI Unit of angle is Radians (rad).
(b) A physical quantity which has neither unit nor dimension is a strain.
The strain is dimensionless quantity.
Also, the strain has no unit.
(c) A constant which has a unit is the speed of light in a vacuum (c)
We know that the speed of light in vacuum is a constant, value given below
And has a unit of meter per second that is the unit of speed.
(d) A constant which has no unit is proton to electron mass ratio.
In physics, the dimensionless physical constant has no units.
Hence is dimensionless and also is unit less.
Hence proton to electron mass ratio is dimensionless constant along with no unit.
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An artificial satellite is revolving around a planet of mass M and radius R, in a circular orbit of radius r. From Kepler’s Third law about the period of a satellite around a common central body, square of the period of revolution T is proportional to the cube of the radius of the orbit r. Show using dimensional analysis, that
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Physics - Exemplar