The $50\,kg$ homogeneous smooth sphere rests on the $30^{\circ}$ incline $A$ and bears against the smooth vertical wall $B$. Calculate the contact forces at $A$ and $B.$

• A

  $N _{ A }=\frac{1000}{\sqrt{3}}\,N , \quad N _{ B }=\frac{500}{\sqrt{3}}\,N$

• B

  $N_B=\frac{1000}{\sqrt{3}}\,N, \quad N_A=\frac{500}{\sqrt{3}}\,N$

• C

  $N_A=\frac{100}{\sqrt{3}}\,N, \quad N_B=\frac{500}{\sqrt{3}}\,N$

• D

  $N _{ A }=\frac{1000}{\sqrt{3}}\,N , \quad N _{ B }=\frac{50}{\sqrt{3}}\,N$