Choose the correct statement.
(i) In Fig. 6.21 three vessels P, Q and R are joined by tubes near their bases. Vessel R is filled with water. When pouring stops, the level of water will be — (a) highest in P, (b) highest in Q, (c) highest in R, (d) equal in all three vessels.
(ii) A rubber sucker (M) is pressed on a flat smooth surface and an identical sucker (N) on a rough surface — (a) both stick, (b) neither sticks, (c) M sticks but N does not, (d) M does not stick but N does.
(iii) A water tank is on a roof at height H. To get water at more pressure on the ground floor, one has to — (a) increase H, (b) decrease H, (c) use a tank of the same height holding more water, (d) use a tank of the same height holding less water.
(iv) Two vessels A and B contain water to the same level (Fig. 6.22), B being the wider. P and F are the pressure and the force at the bottom — (a) P_A = P_B, F_A = F_B, (b) P_A = P_B, F_A < F_B, (c) P_A < P_B, F_A = F_B, (d) P_A > P_B, F_A > F_B.
Hint. Every part turns on the same fact: liquid pressure depends on the height of the column.
(i) Answer: (d) equal in all three vessels.
The three vessels are joined by tubes near their bases, so they form one connected body of water. Water flows between them until the pressure at the joins is the same, and since the pressure exerted by a liquid in a vessel depends on the height of its column, that happens when the heights are equal. The vessels have different shapes and widths, and it makes no difference — exactly as the two pipes of Activity 6.1 gave equal bulges despite different diameters.
(ii) Answer: (c) M will stick but N will not stick.
A sucker works by a pressure difference: pressing it out expels most of the air, the pressure of air surrounding the sucker is higher than the pressure exerted by the air inside, and the outside air holds it on. On a rough surface, air leaks back in through the gaps between the cup and the surface, the inside pressure rises to match the outside, the difference vanishes, and N falls off. This is why Activity 6.4 specifies a smooth flat surface.
(iii) Answer: (a) increase the height 'H' at which the tank is placed.
Pressure depends on the height of the water column above the tap, not on the amount of water. Options (c) and (d) change how much water the tank holds while keeping the same height — which changes nothing at all. Option (b) would make matters worse.
(iv) Answer: (b) P_A = P_B, F_A < F_B.
| Reasoning | |
|---|---|
| Pressure | Both vessels are filled to the same level, and pressure depends only on the height of the column. So P_A = P_B |
| Force | Force = pressure × area. The pressures are equal, but B has the larger base, so F_B > F_A, that is F_A < F_B |
✦ Part (iv) is the one that separates students who have understood from those who have memorised. It requires holding two ideas at once: equal pressures and unequal forces, in the same pair of vessels. If you remember only 'pressure depends on height' you will pick (a); if you remember only 'more water pushes harder' you will pick (d). The formula Pressure = Force ÷ Area, rearranged as Force = Pressure × Area, gives both answers at once.
