Question 1 of 18intermediate💡 UnderstandLong Answer5 marks

Explain why (a) The blood pressure in humans is greater at the feet than at the brain (b) Atmospheric pressure at a height of about 6 km decreases to nearly half of its value at the sea level, though the height of the atmosphere is more than 100 km (c) Hydrostatic pressure is a scalar quantity even though pressure is force divided by area.

(a)
Answer

The blood pressure in humans is greater at the feet than at the brain because pressure depends on the vertical distance (h) between points. According to the relation P = Pa + ρgh, pressure increases with depth. Since the feet are at a lower level than the brain, the column of blood above the feet is longer, resulting in greater pressure at the feet due to the weight of the blood column.

(b)
Answer

If the density of air were constant, the atmosphere would extend only about 8 km (as calculated in Example 9.3). However, in reality, the density of air decreases with height. Gases exhibit large variations in density with changes in pressure and temperature. Most of the atmospheric mass is concentrated near the Earth's surface. Therefore, atmospheric pressure drops to nearly half within the first 6 km, even though the atmosphere extends over 100 km with decreasing pressure.

(c)
Answer

Hydrostatic pressure is a scalar quantity because, although pressure is defined as force divided by area, the directional properties cancel out. Force is a vector quantity, and area can also be treated as a vector (acting normal to the surface). When a vector (force) is divided by another vector (area), the result is a scalar. Additionally, at any point inside a fluid, pressure acts equally in all directions, confirming its scalar nature. The table also lists Pressure as a scalar quantity.

Explanation

This question tests understanding of pressure in fluids. Part (a) applies the hydrostatic pressure formula P = Pa + ρgh to blood circulation. Part (b) addresses the non-uniform density distribution in the atmosphere, which causes rapid pressure decrease near the surface. Part (c) clarifies the scalar nature of pressure through vector analysis and the isotropic property of fluid pressure.