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
Regards
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