Respuesta :
Answer:
n=-1 and m=2
Explanation:
A particle is moving uniformly with acceleration "a"
Uniform speed is v
And radius of circle is r
The acceleration is proportional to
r^n and v^m
i.e
a∝ rⁿ
a ∝v^m
Combing the two
Then, a∝rⁿv^m
Let k be constant of proportionality
Then, a=krⁿv^m. Equation 1
So, we know that the centripetal acceleration keeping an object in circular path is given as
a=v²/r
Rearranging
a=v²r^-1. Equation 2
So comparing this to the proportional
Equating equation 1 and 2
krⁿv^m = v²r^-1
This shows that,
k=1
rⁿ = r^-1
Then, n =-1
Also, v^m =v²
Then, m=2
Therefore,
n=-1 and m=2
Answer:
m=2
n= -1
a=Kv²/r
Explanation:
using dimensional analysis
V = meter/second = m/s
r = meter = m
a = meter/second²=m/s²
If a is proportional to r^n v^m
we have a=r^n v^m =(m)^n (m/s)^m = m/s²
from law of indices;
m^n+m/s^m =m/s²
using system of equations
n+m=1
m=2
so n= -1
then a=kr^n v^m
a=Kv²/r