Question

In non-uniform circular motion, the ratio of tangential to radial acceleration is (r = radius, a = angular acceleration and v = linear velocity)

Options

• `("r"alpha)/"v"`

• `"v"^2/("r"alpha)`

• `("r"alpha^2)/"v"^2`

• `("r"^2alpha)/"v"^2`

Answer 1

`("r"^2alpha)/"v"^2`

Explanation:

In a non-uniform circular motion, the tangential acceleration, `"a"_"t"="dv"/"dt""r"alpha`       ...(i)

and the radial acceleration, `"a"_"r"="V"^2/"r"`   ...(ii)

So. from Eqs. (i) and (ii), we get

`"a"_"t"/"a"_"r"=(("r"alpha)/"V"^2)/"r"=("r"^2alpha)/"V"^2`