An `L` shaped uniform rod of mass `2M` and length `2L (AB = BC = L)` is held as shown in Fig. with a string fixed between `C` and wall so that `AB` is vertical and `BC` is horizontal. There is no friction between the hinge and the rod at `A`.
What will be the reaction between hinge and rod at point `A`?

Options

A. `sqrt(65)(Mg)/4`
B. `2Mg`
C. `sqrt(17)(Mg)/4`
D. `sqrt(17)(Mg)/2`

Answer

D

Explanation

`T_(1)=2M,T_(2)=T=(Mg)/2`
Net reaction `=sqrt(T_(1)^(2)+T_(2)^(2))=sqrt((2Mg)^(2)+(Mg/2)^(2))=(sqrt(17_Mg))/2`