Which of these have no dimensions? Relative density, coefficient of friction, efficiency of a…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Which of these have no dimensions? Relative density, coefficient of friction, efficiency of a machine, angular velocity, solid angle, frequency, and in a decay .
Need a reminder? The key ideaShow
The dimensions of a quantity are the powers of , and in it, found from any formula for it: multiplying adds the powers, dividing subtracts them, and pure numbers have none.
A ratio of two quantities of the same kind is a pure number.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Ratios. Relative density (density over density), coefficient of friction (force over force), efficiency (energy over energy), solid angle (area over area) and (time over time) are pure numbers.
Step 2. The others. Angular velocity and frequency are both .
Answer: of them: relative density, coefficient of friction, efficiency, solid angle and .
Watch out. A unit name does not mean a dimension: the steradian (solid angle) and the radian are names for pure numbers.
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