A vertical off-shore structure is built to withstand a maximum stress of 10⁹Pa. Is the structure suitable for putting up on top of an oil well in the ocean ? Take the depth of the ocean to be roughly 3 km, and ignore ocean currents.
Toricelli’s barometer used mercury. Pascal duplicated it using French wine of density984 kg m–³. Determine the height of the wine column for normal atmospheric pressure.
A 50 kg girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter 1.0 cm. What is the pressure exerted by the heel on the horizontal floor ?
Explain why
(a) To keep a piece of paper horizontal, you should blow over, not under, it
(b) When we try to close a water tap with our fingers, fast jets of water gush
through the openings between our fingers
(c) The size of the needle of a syringe controls flow rate better than the thumb
pressure exerted by a doctor while administering an injection
(d) A fluid flowing out of a small hole in a vessel results in a backward thrust on
the vessel
Fill in the blanks using the word from the list appended with each statement:
(a) Surface tension of liquids generally … with temperatures (increases / decreases)
(b) Viscosity of gases … with temperature, whereas viscosity of liquids … with
temperature (increases / decreases)
(c) For solids with elastic modulus of rigidity, the shearing force is proportional
to … , while for fluids it is proportional to … (shear strain / rate of shear
strain)
(d) For a fluid in a steady flow, the increase in flow speed at a constriction follows
(conservation of mass / Bernoulli’s principle)
(e) For the model of a plane in a wind tunnel, turbulence occurs at a … speed for
turbulence for an actual plane (greater / smaller)
Explain why
(a) The angle of contact of mercury with glass is obtuse, while that of water with glass is acute.
(b) Water on a clean glass surface tends to spread out while mercury on the
same surface tends to form drops. (Put differently, water wets glass while
mercury does not.)
(c) Surface tension of a liquid is independent of the area of the surface
(d) Water with detergent disolved in it should have small angles of contact.
(e) A drop of liquid under no external forces is always spherical in shape
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.
The average depth of Indian Ocean is about 3000 m. Calculate the fractional compression, ∆V/V, of water at the bottom of the ocean, given that the bulk modulus of water is 2.2 × 10⁹ N m–2. (Take g = 10 m s–2)
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