Question

The $50kg$ homogeneous smooth sphere rests on the incline $A$ and bears the smooth vertical wall $B$. calculate the contact forces at $A$ and $B$.

Answer 1

By Lami's theorem
$\begin{array}{c}\frac{mg}{\sin {120}^{\circ }}=\frac{R_1}{\sin (90+60)}=\frac{R_2}{\sin {90}^{\circ }}\\ \underset{1}{\underset{}{\frac{50\times 10}{\sin {(90+30)}^{\circ }}}}=\underset{2}{\underset{}{\frac{R_1}{\cos 60}}}=\underset{3}{\underset{}{\frac{R_2}{1^{\circ }}}}\\ from\left(1\right)and\left(3\right)\\ R_2=\frac{1000}{\sqrt{3}}N\\ from\left(2\right)and\left(3\right)\\ R_1=\frac{500}{\sqrt{3}}\end{array}$