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A smooth block is released at rest on a $45^{\circ}$ incline and then slides a distance d. The time taken to slide is $\mathrm{n}$ times as much to slide on rough incline than on a smooth incline. The coefficient of friction is
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The correct answer is:
$\mu_{\mathrm{k}}=1-\frac{1}{\mathrm{n}^2}$
$\mu_{\mathrm{k}}=1-\frac{1}{\mathrm{n}^2}$
$\mathrm{d}=\frac{1}{2} \frac{\mathrm{g}}{\sqrt{2}} \mathrm{t}_1^2$
$\mathrm{~d}=\frac{1}{2} \frac{\mathrm{g}}{\sqrt{2}}\left(1-\mu_{\mathrm{k}}\right) \mathrm{t}_2^2$
$\frac{\mathrm{t}_2^2}{\mathrm{t}_1^2}=\mathrm{n}^2=\frac{1}{1-\mu_{\mathrm{k}}}$
$\mathrm{~d}=\frac{1}{2} \frac{\mathrm{g}}{\sqrt{2}}\left(1-\mu_{\mathrm{k}}\right) \mathrm{t}_2^2$
$\frac{\mathrm{t}_2^2}{\mathrm{t}_1^2}=\mathrm{n}^2=\frac{1}{1-\mu_{\mathrm{k}}}$
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