A) 3/5
B) 3/4
C) 4/5
D) 2/3
Correct Answer: B
Solution :
The angle at which the block just begins to slide is the angle of repose. In terms of angle of repose, we know\[\mu =\tan \theta \]. So we must first calculate\[\tan \theta \]. It is given that inclination of the plane is\[3\]in\[5\],\[i.e.\]\[\sin \theta =\frac{3}{5}\]. Now we are given \[\sin \theta \] and are required to calculate\[\tan \theta \]. We can either calculate it using the calculator by first calculating sin inverse of \[\frac{3}{5}\] and then calculating its tan, or it can also be \[5\] calculated by applying simple trigonometry, as follows: \[\sin \theta =\frac{3}{5}\], it means that perpendicular side of the triangle is \[3\] units and hypotenuse side of the triangle is \[5\] units. So, base of the triangle\[=\sqrt{{{5}^{2}}-{{3}^{2}}}=4\,\,units\] \[\therefore \] \[\tan \theta =\frac{perpendicular}{base}=\frac{3}{4}\]
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