Answer to Question #135383 in Classical Mechanics for Sofia rose

Question

A student taking a quiz finds on a reference sheet the two equations f = 1 / T and =square root of (1/T).
She has forgotten what T represents in each question.
Use dimensional analysis to determine the units required for T in each question.
Explain how you can identify the physical quantity each T represents from the units.

Answer 1

solution

given formula

$f=\frac{1}{T}$

f is the frequency so unit of frequency is $s^{-1}$

by using dimension analysis

$T=\frac{1}{f}$

so

$[ \quad T\quad]=\frac{1}{s^{-1}}$

=s.

so unit of T is second and T is time.

$v=\sqrt \frac{T}{\mu}$

and v is velocity and mu is linear density

$T=v^2\mu$

$[\quad T\quad]=[\quad v^2\mu \quad]$

$[\quad T\quad]=m^2/s^2\cdot kg/m\\$

$[\quad T\quad]=\frac{kg\cdot m}{s^2}=N$

there T represents force.