Question

A student has derived the following nondimensionally homogeneous equation: a=x/t2-vt+F/m where v is a velocity's magnitude , a is an acceleration's magnitude, t is a time, m is a mass, F is a force's magnitude , and x is a distance (or length). Which terms are dimensionally homogeneous? .

a) x/t
b) vt
c) a
d) F/m

Answer 1

Letter C) and D) is the correct answer.

Step-by-step explanation:

We know that the a is an acceleration's magnitude, so the units of a are m/s².

Now, let's analyze each terms. If we want that each term will be dimensionally homogeneous, all of them must have the same units of a.

`[(x)/(t)]=[(m)/(s)]`

`[vt]=[m]`

`[(F)/(m)]=[(N)/(kg)]=[kg(m)/(s^(2)kg)]=[(m)/(s^(2))]`

Therefore, the term F/m is the correct answer.

I hope it helps you!