A $2 \mathrm{~kg}$ brick begins to slide over a surface which is inclined at an angle of $45^{\circ}$ with respect to horizontal axis. The co-efficient of static friction between their surfaces is:
JEE MAIN 2024, Difficult
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$\mathrm{mg} \sin 45=\mathrm{f}_{\mathrm{L}}$
$\mathrm{mg} \cos 45=\mathrm{N}$
$\mathrm{f}_{\mathrm{L}}=\mu_{\mathrm{x}} \mathrm{N}$
$\mu_{\mathrm{x}}=\tan 45=1$
or
$\tan \theta=\mu_{\star}$ ( $\theta$ is angle of repose)
$\tan 45=\mu_\alpha=1$
correct option $(1)$
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