Question

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

• A. $N_A=\frac{1000}{\sqrt{3}}N,N_B=\frac{500}{\sqrt{3}}N$
• B. $N_B=\frac{1000}{\sqrt{3}}N,N_A=\frac{500}{\sqrt{3}}N$
• C. $N_A=\frac{500}{\sqrt{3}}N,N_B=\frac{500}{\sqrt{3}}N$
• D. $Noneofthese$

Answer 1

The correct option is A $N_A=\frac{1000}{\sqrt{3}}N,N_B=\frac{500}{\sqrt{3}}N$

$N_B=N_A\sin {30}^0$

$\Rightarrow N_B=\frac{N_A}{2}$

$\Rightarrow N_B=\frac{500}{\sqrt{3}}N$

$N_A\cos {30}^0=Mg$

$N_A\times \frac{\sqrt{3}}{2}=50\times 10$

$N_A=\frac{1000}{\sqrt{3}}N$