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:

• A

  $1.7$
• B

  $\frac{1}{\sqrt{3}}$
• C

  $0.5$
• Correct answer
  D

  $1$

Solution

$\begin{aligned} & \mathrm{mg} \sin 45=\mathrm{f}_{\mathrm{L}} \\ & \mathrm{mg} \cos 45=\mathrm{N} \\ & \mathrm{f}_{\mathrm{L}}=\mu_{\mathrm{s}} N \\ & \mu_{\mathrm{s}}=\tan 45=1 \end{aligned}$ or $\tan \theta=\mu_s$ ( $\theta$ is angle of repose) $\tan 45=\mu_{\mathrm{s}}=1$

Hence, the correct answer is option: 'D'.