A spherical ball of iron of radius 2 mm is falling through a column of glycerine. If densities of glycerine and iron are respectively 1.3 × 10³kg/m³ and 8 × 10³ kg/m³. η for glycerine= 0.83 Nm^-2 sec, then the terminal velocity is

0.7 m/s
0.07 m/s
0.007 m/s
0.0007 m/s

Solution

Terminal velocity,\(V_{0}=\frac{2r^{2}(\rho -\rho \: 0)g}{9\eta }\)

=\(\frac{2\times (2\times 10^{-3})^{2}\times (8-1.3)\times 10^{3}\times 9.8}{9\times 0.83}= 0.07ms^{-1}\)

A rain drop of radius 0.3 mm has a terminal velocity in air =1 m/s. The viscosity of air is 8 × 10^-5 poise. The viscous force on it is

45.2 × 10^-4dyne
101.73×10^-5dyne
16.95 × 10^-4dyne
16.95 × 10^-5dyne

Solution

\(F=6\pi \eta rv\)

= 6 × 3.14 × (8 × 10^-5) × 0.03 × 100 = 4.52 × 10^-3 dyne

A cylinder is filled with non-viscous liquid of density d to a height h₀ and a hole is made at a height h₁from the bottom of the cylinder. The velocity of the liquid is suing out of the hole is

\(\sqrt{2gh_{0}}\)
\(\sqrt{2gh_{0}}\)
\(\sqrt{2g(h_{1})}\)
\(\sqrt{2g(h_{1})}\)

Solution

Velocity of liquid flowing out of hole =\(\sqrt{2gh}\)
Here h = (h₀– h₁)

The terminal velocity depends upon

\(\frac{1}{r}\)
\(\frac{1}{r^{2}}\)
\(\frac{1}{r^{3}}\)
\(r^{2}\)

Solution

Terminal velocity,\(V_{T}=\frac{2r^{2}g}{9\eta }(\rho -\sigma ),V_{T}\alpha r^{2}\)

The velocity of efflux of a liquid through an orifice in the bottom of the tank does not depend upon

size of orifice
height of liquid
acceleration due to gravity
density of liquid

Solution

v=velocity of efflux through an orifice=\(\sqrt{2gh}\)

It is independent of the size of orifice.

At the boiling point of a liquid, surface tension

is zero
is infinite
is same as that at any other temperature
cannot be determined

The surface energy of a liquid drop of radius r is proportional to

r³
πr²
r
\(\frac{1}{r}\)

Solution

Surface energy ∝ surface area = πr²

A liquid is contained in a vessel. The liquid-solid adhesive force is very weak as compared to the cohesive force in the liquid. The shape of the liquid surface will be

horizontal
vertical
concave
convex

Two liquids drops coalesce to form a large drop. Now,

energy is liberated
energy is neither liberated nor absorbed
some mass gets converted into energy
energy is absorbed

Solution

When liquid drops coalesce, there is a decrease of surface area and therefore decrease of surface energy.Hence, energy is liberated.

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

rise alittle
falla little
remain stationary
none of these

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