A wooden plank of length 1 m and uniform cross-section is hinged at one end to the bottom of a

step 1 Hi everyone we have OA is equal to Oc y2 that is 0 .5 upon 2 cost of theta. Ro is mass per unit

A wooden plank of length 1 m and uniform cross-section is...

A wooden plank of length $1 \mathrm{~m}$ and uniform cross-section is hinged at one end to the bottom of a tank as shown in Fig. $8.48$. The tank is filled with water up to a height of $0.5 \mathrm{~m}$. The specific gravity of the plank is $0.5$. The angle $\theta$ in radian that the plank makes with the vertical in the equilibrium position is $\frac{\pi}{n}$, then the value of $n$ is.

Key Concepts

Moments Equilibrium

Moments equilibrium refers to the condition where the sum of all torques acting about a pivot point is zero. This concept is fundamental when analyzing the balance of forces in systems with hinges, ensuring that rotational forces due to weight and buoyant pressure are balanced.

Specific Gravity

Specific gravity is a comparison of the density of a substance to that of a reference substance, typically water. It plays a critical role in determining the weight of an object relative to the buoyant force exerted by the fluid, influencing the overall equilibrium conditions.

Buoyancy Force

Buoyancy force, based on Archimedes' principle, is the upward force exerted by a fluid that opposes the weight of an immersed object. In equilibrium problems involving submerged bodies, understanding how this force interacts with gravitational forces is crucial.

Center of Pressure

The center of pressure is the point on a submerged surface where the total sum of the pressure field is considered to act. It is important for calculating the moment due to the fluid forces, as it indicates the effective application point of the hydrostatic force.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at rest due to the force of gravity. This pressure increases linearly with depth and is essential when determining the force acting on submerged surfaces, such as the part of the plank that is underwater.

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