Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
Which of these pairs have the same dimensions? (a) impulse and momentum, (b) frequency and angular velocity, (c) surface tension and spring constant, (d) force and pressure, (e) energy per volume and pressure.
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.
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. (a) Both . (b) Both .
Step 2. (c) Both . (e) Both .
Step 3. (d) Force is , pressure : they differ by an area.
Answer: (a), (b), (c) and (e) match; (d) does not. So pairs match.
Watch out. Matching dimensions does not make two quantities the same thing. A spring constant and a surface tension describe very different objects.
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