An $L$-shaped elastic member $\text{ABC}$ with slender arms $\text{AB}$ and $\text{BC}$ of uniform cross-section is clamped at end $A$ and connected to a pin at end $C$. The pin remains in continuous contact with and is constrained to move in a smooth horizontal slot. The section modulus of the member is same in both the arms. The end $C$ is subjected to a horizontal force $P$ and all the deflections are in the plane of the figure. Given the length $AB$ is $4a$ and length $BC$ is $a$, the magnitude and direction of the normal force on the pin from the slot, respectively, are
- $\frac{3P}{8}$, and downwards
- $\frac{5P}{8}$, and upwards
- $\frac{P}{4}$, and downwards
- $\frac{3P}{4}$, and upwards