A block takes $$t$$ time to slide down a plane inclined at 45° to the horizontal. If the surface is made smooth (frictionless), the block takes time $$\dfrac{t}{2}$$ to slide down the plane. The coefficient of friction between the block and the inclined plane is $$\left(\dfrac{\alpha}{100}\right)$$. The value of $$\alpha$$ is __________.

On a smooth plane: $$a_{\text{smooth}} = g \sin\theta$$

On a rough plane: $$a_{\text{rough}} = g \sin\theta - \mu g \cos\theta$$

$$\frac{t_{\text{rough}}}{t_{\text{smooth}}} = \sqrt{\frac{a_{\text{smooth}}}{a_{\text{rough}}}}$$

$$\frac{t}{\frac{t}{2}} = \sqrt{\frac{g \sin 45^\circ}{g \sin 45^\circ - \mu g \cos 45^\circ}}$$

$$2 = \sqrt{\frac{\frac{1}{\sqrt{2}}}{\frac{1}{\sqrt{2}} - \mu \frac{1}{\sqrt{2}}}} = \sqrt{\frac{1}{1 - \mu}}$$

$$4 = \frac{1}{1 - \mu}$$

$$4 - 4\mu = 1 \implies 4\mu = 3 \implies \mu = \frac{3}{4} = 0.75$$

$$\frac{\alpha}{100} = 0.75 \implies \alpha = 75$$