Fluid Mechanics

Statement 'a' is a false statement. Thus, it is the correct option. The pressure exerted by a liquid increases with the increase in depth inside the liquid.

Surface tension is the cohesive force between liquid molecules that causes water droplets to minimize their surface area. A sphere has the minimum surface area for a given volume, which is why small water droplets naturally form spherical shapes.

Water potential (Ψ) is the sum of its components. In plant physiology, Ψ = Ψs + Ψp, where Ψs (or yw) is solute potential (osmotic potential) and Ψp (or yp) is pressure potential (turgor pressure). Option D shows this relationship correctly (ys + yp, using subscripts for solute and pressure). Options A, B, and C are incorrect representations of the water potential equation.

Bar is a metric unit of pressure equal to 100,000 Pa (pascals). It is commonly used to express atmospheric pressure, where 1 bar is approximately equal to Earth's atmospheric pressure at sea level. It is not specifically for water pressure or buoyant force, though it can measure any pressure.

Surface tension minimizes the surface area of a liquid for a given volume, causing water droplets to become spherical (a sphere has minimum surface area). Atmospheric pressure and gravitational force act externally, while 'capillary rice' is a typo for 'capillary rise' (a different phenomenon).

Water reaches its maximum density at approximately 4°C (39°F). This unusual property occurs because water molecules form a highly ordered structure as temperature decreases from 4°C to 0°C, causing expansion. This property is crucial for aquatic life as ice floats, insulating the water below and allowing organisms to survive under frozen surfaces.

This is the correct option. Ice floats because it is about 9% less dense than liquid water. In other words, ice takes up about 9% more space than water. The heavier water displaces the lighter ice, so ice floats to the top.  

Total volume of water displaced = (4 x 50) m³ = 200 m³  Rise in water level = 200/800 = 0.25 m = 25 cm

According to Archimedes' principle, the fraction of a floating object submerged depends on the ratio of the object's density to the liquid's density. The mass of the ball is irrelevant - only the densities matter. For a given liquid density, balls with the same density will float at the same level regardless of mass.

According to Archimedes' principle, an object immersed in a fluid experiences an upward buoyant force equal to the weight of the displaced fluid. When the jug is in the bucket of water, the buoyant force reduces its apparent weight. When removed from water, this force disappears and the full weight is felt.

For a floating body, the fraction submerged equals the ratio of densities: fraction_submerged = density_iceberg / density_water. Here: 0.93/1.03 = 0.9029, meaning about 90.29% is submerged. The visible (above water) fraction is 1 - 0.9029 = 0.0971 or 9.71%, which rounds to approximately 11%. Option B is closest.

Oil spreads on water because water's high surface tension creates a strong 'skin' effect. Oil has much lower surface tension, allowing it to form a thin film across the water surface. Density (option A) and viscosity (option B) are secondary factors.

Yes, it is the density of water.

When the bottle is swung, the liquid is pushed outward by centrifugal force. The air bubbles, being less dense than the liquid, are displaced toward the region of lower pressure, which is the center of rotation (the neck).

According to Archimedes' principle, the weight lost by an object immersed in a fluid is equal to the weight of the fluid displaced. If the weight lost is the same, the volume of fluid displaced must be the same, which implies the objects have the same volume.