Pressure, Winds, Storms, and Cyclones

Correct option: (d) equal in all three vessels

Justification: Liquids find their own level when connected to each other. Since all three vessels P, Q, and R are connected at the bottom (communicating vessels), the water level will equalise and become the same in all three vessels, regardless of their shapes or sizes. This is a direct consequence of the principle that liquid pressure depends only on the height of the liquid column, not on the shape or volume of the container.

Correct option: (c) M will stick but N will not stick.

Justification: A rubber sucker works by expelling air from between its cup and the surface, creating a low-pressure region inside. The higher atmospheric pressure outside then holds it firmly to the surface. This works only on a smooth, flat surface where a proper airtight seal can be formed. On a rough surface, air leaks in through the gaps, so the pressure inside equals the atmospheric pressure outside, and the sucker does not stick. Hence, M (on smooth surface) sticks but N (on rough surface) does not.

Correct option: (a) increase the height 'H' at which the tank is placed.

Justification: The pressure exerted by a liquid depends on the height of the liquid column above the point of measurement. The greater the height 'H' of the water tank above the ground floor, the greater the pressure of water at the taps on the ground floor. Increasing 'H' increases the height of the water column, thereby increasing the water pressure.

**Correct option: (b) $\mathrm{P_A} = \mathrm{P_B},\ \mathrm{F_A} < \mathrm{F_B}$

Justification:
- Pressure at the bottom of a liquid column depends only on the height of the liquid column (not on the shape or base area of the vessel). Since both vessels have water up to the same level**, the pressure at the bottom is equal: $P_A = P_B$.
- Force = Pressure × Area. Since vessel B has a larger base area than vessel A (as seen from Fig. 6.22 where B is wider), the force exerted at the bottom of B is greater: $F_A < F_B$.

Thus, $P_A = P_B$ and $F_A < F_B$.

(i) True [T]
Air always moves from a region of higher pressure to a region of lower pressure. This pressure difference is the primary cause of wind formation.

(ii) False [F]
Liquids exert pressure not only at the bottom of a container but also on the sides (walls) of the container. In fact, liquids exert pressure in all directions.

(iii) False [F]
The eye of a cyclone is the calm, clear centre of the storm. The weather at the eye is calm and clear, not stormy. The stormy conditions (strong winds, heavy rain) exist in the region surrounding the eye.

(iv) True [T]
During a thunderstorm, it is safer to be inside a car (with windows closed) than to be in the open. The metal body of the car acts as a Faraday cage and conducts the lightning charge safely to the ground, protecting the occupants inside.

Given:
- Fig. 6.23a: Boy lying horizontally on sand (large contact area).
- Fig. 6.23b: Boy standing vertically on sand (small contact area — only feet touching).
- The weight (force) of the boy is the same in both cases.

Concept used:
$$\text{Pressure} = \frac{\text{Force}}{\text{Area}}$$

Reasoning:
- When the boy lies horizontally, his body is spread over a large area of the sand. The same weight is distributed over a larger area, so the pressure exerted on the sand is less.
- When the boy stands vertically, only his feet are in contact with the sand, which is a much smaller area. The same weight is now concentrated over a smaller area, so the pressure exerted on the sand is much greater.

Conclusion: The boy sinks more in sand when standing vertically (Fig. 6.23b), because the pressure exerted on the sand is greater due to the smaller contact area.

Given:
- Weight of elephant (Force) $= 20000\ \text{N}$
- Area covered by one foot $= 0.25\ \text{m}^2$
- Number of feet $= 4$

Step 1: Calculate total area of contact.
$$\text{Total Area} = 4 \times 0.25 = 1.0\ \text{m}^2$$

Step 2: Apply the formula for pressure.
$$\text{Pressure} = \frac{\text{Force}}{\text{Area}}$$

$$\text{Pressure} = \frac{20000\ \text{N}}{1.0\ \text{m}^2}$$

$$\boxed{\text{Pressure} = 20000\ \text{N/m}^2 = 20000\ \text{Pa}}$$

Answer: The pressure exerted by the elephant on the ground is $\mathbf{20000\ Pa}$ (or $20000\ \text{N/m}^2$).

Given:
- Boat A: Base area $= 7\ \text{m}^2$, Number of persons $= 5$
- Boat B: Base area $= 3.5\ \text{m}^2$, Number of persons $= 3$
- Weight of each person $= 700\ \text{N}$

Step 1: Calculate total force (weight) on each boat.
$$F_A = 5 \times 700 = 3500\ \text{N}$$
$$F_B = 3 \times 700 = 2100\ \text{N}$$

Step 2: Calculate pressure on the base of each boat.
$$P_A = \frac{F_A}{\text{Area}_A} = \frac{3500}{7} = 500\ \text{N/m}^2$$
$$P_B = \frac{F_B}{\text{Area}_B} = \frac{2100}{3.5} = 600\ \text{N/m}^2$$

Step 3: Compare the pressures.
$$P_B - P_A = 600 - 500 = 100\ \text{N/m}^2$$

Conclusion: Boat B experiences more pressure on its base. The pressure on Boat B is greater than on Boat A by $\mathbf{100\ \text{N/m}^2}$ (i.e., $100\ \text{Pa}$).