Although the solution to this is already available but i have doubt in it... so kindly solve it in the best possible way
Q. A wooden plate is hinged at one bottom end of a container and then the container is filled with water up to a height of 0.5 m. The specific gravity and length of the plate is 0.5 and 1 m respectively. The angle which the wooden plate makes with the vertical in equilibrium position is


A. 20 °
B. 30 °
C. 45 °

Dear Student ,
up to what height water is filled .In  question you forgot mention it , i think it should be .5m
 
 
For equilibrium Fnet. = 0 and τnet = 0

 
 
Taking moment about O
 
mg x ℓ / 2 sin( θ )= FT (ℓ - x / 2 ) sin (θ )…. (i)
 
Also FT = wt. of fluid displaced = [(ℓ - x )] x ρw g …(ii)
 
And m = (ℓ A) 0.5 ρw … (iii)
 
Where A is the area of cross section of the rod
 
From (i), (ii) and (iii)
 
(ℓ A) 0.5 ρw g x ℓ/ 2 sin θ = [(ℓ - x) A] ρw g x (ℓ - x / 2) sin θ
 
Here, ℓ = 1 m
 
∴ (1 – x )2 = 0.5 ⇒ x = 0.293 m
 
From the diagram
 
cos θ = 0.5 / 1 – x = 0.5 / 0.707 ⇒ θ = 45°

Regards

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