During a laboratory test on a grain pile, paddy grains are discharged on a horizontal circular disc of diameter $0.60\text{ m}$. The grains form a conical heap of height $0.18\text{ m}$ covering the entire disc surface. The angle of repose of the paddy grains in degrees is ________ (round off to 1 decimal place).
Answer Key:
31.0
Step-by-Step Solution & Explanation
The angle of repose $\theta$ of a conical grain heap is given by:
$\tan \theta = \frac{h}{r}$
Where:
• Cone height $h = 0.18\text{ m}$
• Base radius $r = \frac{0.60}{2} = 0.30\text{ m}$
$\tan \theta = \frac{0.18}{0.30} = 0.60$
$\theta = \tan^{-1}(0.60) \approx 30.9638^\circ \approx 31.0^\circ$