In a non - uniform circular motaion the ratio of tangential to radial acceleration is (where, r= radius of circle, v= speed of the particle, `alpha=` angular acceleration)

Options

A. `(alpha^(2)r^(2))/(v)`
B. `(alpha^(2)r)/(v^(2))`
C. `(alphar^(2))/(v^(2))`
D. `(v^(2))/(r^(2)alpha)`

Answer

C

Explanation

Given, radius of circle = r
Speed of particel = v
Angular acceleration = `alpha`
We known that, tangential acceleration `=alphar` . .. (i)
Radial acceleration `(v^(2))/(r)` . . .(ii)
On dividing Eq. (i) by Eq. (ii), we get
`("Tangential acceleration")/("Radial acceleration")=(alphar)/(v^(2))xxr(alphar^(2))/(v^(2))`