A block starts moving up an inclined plane of inclination 30 ° with...

$AtoB$

${a}_{1} = gsin30 ° + \mu gcos30 °$

$= \dfrac{g}{2} + \dfrac{\mu g\sqrt{3}}{2}; g = 10m{s}^{2}$

${v}_{0}^{2} - 2{a}_{1}\left(s\right) = 0$

$s = {v}_{0}^{2}{a}_{1}$ .....(i)

$BtoA$

${a}_{2} = \dfrac{g}{2} - \dfrac{\mu\sqrt{3}}{2}g$

${\left(\dfrac{{V}_{0}}{2}\right)}^{2} = 2{a}_{2}\left(s\right)$

$s = {V}_{0}^{2}4{a}_{2}$ .....(ii)

From equation (i) and (ii)

${V}_{0}^{2}{a}_{1} = {V}_{0}^{2}4{a}_{2}$

$⇒ {a}_{1} = 4{a}_{2}$

$⇒ 5 + 5\sqrt{3}\mu = 4\left\{5 - 5\sqrt{3}\mu\right\}$

$⇒ 5 + 5\sqrt{3}\mu ⇒ 25\sqrt{3}\mu = 15 ⇒ \mu = \dfrac{\sqrt{3}}{5} = 0 . 346 = \dfrac{346}{1000}$

So, $\dfrac{1}{1000} = \dfrac{346}{1000}$