Question

A house is on built on the top of a hill with ${45}^0$ slope. Due to the sliding of material and sand from top to the bottom of hill, the slope angle has been reduced.
If the coefficient of static friction between sand particles is 0.75, what is the final angle attained by hill? ($ta{n}^{-1}0.75={37}^0$)

• A. $8^0$
• B. ${45}^0$
• C. ${37}^0$
• D. ${30}^0$

Answer 1

The correct option is C ${37}^0$

In equilibrium, when sliding stops

$N=mg\cos \theta \dots \left(1\right)$

And $f=mg\sin \theta =\mu N\dots \left(1\right)$

Dividing $\left(2\right)$ by$\left(1\right)\Rightarrow \mu =\tan \theta =0.75=\frac{3}{4}\Rightarrow \theta =37°$