Equation Dimension Help: Valid Statements for Dimensionally Correct Equations

[am08]

Select ALL the valid statements, i.e., B, AC, BCD. If an equation is dimensionally

A) correct, the equation must be correct.
B) correct, the equation may be wrong.
C) incorrect, the equation may be correct.
D) incorrect, the equation must be wrong.
E) correct, the equation may be correct.

Hint: An equation is dimensionally correct if both sides of the equation have the same dimensions. For instance, the equation x = (1/2)*a*t^2 has the units of length (meters) on both sides, because the units of a*t^2 are (m/s^2)*s^2 = m. The equation x = a*t is dimensionally incorrect, because the units on the left are length (meters), but the units on the right are (m/s^2)*s = m/s, the units of speed.

Which statements are correct?

 

[mgb_phys]

First do you understand what dimensionally correct means?

Can an equation which is dimensionally wrong be correct?
Then try and think of some equations that are dimensionally correct but obviously stupid.

 

[am08]

does it imply that both sides of the equation contain the same units?

 

[mgb_phys]

Yes.
Without giving away the answer to the question, both sides of the equation must contain the same units. You obviously can't have an equation that calculates speed if the units come out as eg mass. So the units of the parts on the right must came out to the units of the answer you want.

It's a very important topic in physics, you can often work out what form an equation is going to have purely from the units. It's also worth knowing how to break down units to the fundamental units of length, mass and time (at least for mechanics type questions).

 

[am08]

I understand the topic but I can't determine the correct answers.. any chance you could help me finish this problem mgb_phys ?

 

[Distortion]

Dimensional analysis can prove very useful. As in this case, which is also pretty cool => http://www.atmosp.physics.utoronto.ca/people/codoban/PHY138/Mechanics/dimensional.pdf"

 

[mgb_phys]

A) correct, the equation must be correct.
B) correct, the equation may be wrong.

What if there is a constant missing?

C) incorrect, the equation may be correct.
D) incorrect, the equation must be wrong.

If the units don't balance can the equation possibly be correct?

E) correct, the equation may be correct.

That shoudl be pretty obvious after answering the previous sets.