Non-Uniform Circular Motion question from MHT CET 2020 (19 Oct, Shift 2)

Answer: (a)

1. After time $t$: $v = at$, so $a_c = \frac{a^2t^2}{r}$
2. Net acceleration: $a_{net} = \sqrt{a^2 + \frac{a^4t^4}{r^2}} = \frac{\sqrt{a^4t^4 + a^2r^2}}{r}$
3. Slipping starts when friction is at maximum: $\mu m g = m a_{net}$
4. $\mu = \frac{\left[a^4t^4 + a^2r^2\right]^{1/2}}{rg}$, so the answer is (a).