True/False: Mechanical Properties of Solids and Fluids - JEE Advanced

Q.1. A man is sitting in a boat which is floating in a pond. If the man drinks some water from the pond, the level of the water in the pond decreases.

Ans. F

Solution. When the man drinks some water from the pond, his weight increases and therefore the boat will sink further. The further sinking of the boat will displace the same volume of water in pond as drunk by man. Therefore, there will no change in the level of water in the pond.

Q.2. A barometer made of a very narrow tube (see Fig) is placed at normal temperature and pressure. The coefficient of volume expansion of mercury is 0.00018 per C° and that of the tube is negligible. The temperature of mercury in the barometer is now raised by 1°C, but  the temperature of the atmosphere does not change.

Then the mercury height in the tube remains unchanged.              (1983 - 2 Marks)

Ans. F

Solution. Pressure P₁ = P₂ = 1 atm = hρg 

Note : On changing the temperature, g will not change and atmospheric pressure will not change. 

∴ h × r = constant.

When temperature is increased, the density of Hg decreases and hence, h increases.

Q.3. Water in a closed tube (see Fig)  is heated with one arm vertically placed above a lamp. Water will begin to circulate along the tube in counter-clockwise direction.               (1983 - 2 Marks)

Ans. F

Solution. When water is heated at end A, the density decreases and the water moves up. This is compensated by the movement of water from B to A i.e., in clockwise direction.

Q.4. A block of ice with a lead shot embedded in it is floating on water contained in a vessel. The temperature of the system is maintained at 0°C as the ice melts. When the ice melts completely the level of water in the vessel rises.        (1986 - 3 Marks)

Ans. F

Solution. When the block of ice melts, the lead shot will ultimately sink in the water. When lead shot sinks, it will displace water equal to its own volume. But when lead shot was embedded in ice, it displaced more volume of water than its own volume because d_lead > d_water. Therefore, level of water will fall.