Hydrostatics
1. State the law of floatation? [1]
Ans01. Law of floatation states that a body will float in a liquid, if weight of the liquid displaced by the immersed part of the body is at least equal to or greater than the weight of the body.
2. The blood pressure of humans is greater at the feet than at the brain? [1]
Ans02. The height of the blood column in the human body is more at the feet than at the brain as since pressure is directly dependent on height of the column, so pressure is more at feet than at the brain.
3. Define surface tension? [1]
Ans03. It is measured as the force acting on a unit length of a line imagined to be drawn tangentially anywhere on the free surface of the liquid at rest
4. State the angle of contact and on what values do the angle of contact depends? [2]
Ans04. Angle of contact between a liquid and a solid is defined as the angle enclosed between the tangents to the liquid surface and the solid surface inside the liquid, both the tangents being drawn at the point of contact of liquid with the solid. It
depends upon:-
1) Upon nature of liquid and solid in contact
2) The Medium which exists above the free surface of liquid.
5. Hydrostatic pressure is a scalar quantity even though pressure is force divided by area, and force is a vector. Explain? [2]
Ans05. Since due to applied force on liquid, the pressure is transmitted equally in all directions, inside the liquid. Since there is no fixed direction for the pressure due to liquid. Hence it is a scalar quantity.
6. Find the work done in blowing a soap bubble of surface tension 0.06 N/m from 2cm radius to 5cm radius? [2]
Ans06.
Here, Surface tension = s = 0.06 N/m
r1 = 2 cm = 0.02 m
r2 = 5 cm = 0.05 m
Since bubble has two surface, initial surface area of the bubble = 2 x 4πr12
= 2 x 4π (0.02)2 = 32π x 10^-4 m2
Final surface of the bubble = 2 x 4πr22 = 2×4π(0.05)2 = 200π x 10^-4 m2
Increase in surface area = 200 π x 10^-4-32 π x 10^-4 m2 = 168π x 10^-4 m2
∴ work done = surface tension x Increase in surface area = 0.06 x 168 π x 10^-4
Work done = 0.003168J
7. Calculate the radius of new bubble formed when two bubbles of radius r1 and r2 coalesce? [3]
Ans07.
Consider two soap bubble of radii r1 and r2 and volumes as v1 and v2. Since bubble is in the form of a sphere: →
If s = surface tension of the soap solution
p1& p2 = excess pressure inside the two soap bubbles
Let r be the radius of the new soap bubble formed when the two soap bubble coalesce under and excess of pressure inside this new soap bubble then
As the new bubble is formed under isothermal condition, so Boyle’s law holds good and hence
8. A liquid drop of diameter 4 mm breaks into 1000 droplets of equal size. Calculate the resultant change in the surface energy. Surface tension of the liquid is 0.07 N/m?
Ans08:
Since the diameter of drop = 4 mm
Radius of drop = 2 mm = 2 x 10^-3 m
S = Surface tension = 0.07 N/m
Let r be the radius of each of the small droplets
volume of big drop = 1000 x volume of the small droplets
Increase in surface area,
9. State the principle on which Hydraulic lift work and explain its working? [5]
Ans09:
Hydraulic lift works on the principle of the Pascal’s law. According to this law, in the absence of gravity, the pressure is same at all points inside the liquid lying at the same horizontal plane.
Working of Hydraulic effect:→
a = Area of cross –section of piston at C
A = Area of cross – section of piston at D.
Let a downward force f be applied on the piston C. Then the pressure exerted on the liquid, P = F / a
According to Pascal’s law, this pressure is transmitted equally to piston of cylinder D.
∴ Upward fore acting on the piston of cylinder D will be :→
F = P A
= (f / a) x A
As A ≫ a, F ≫f
i.e. small fore applied on the smaller piston will be appearing as a very large force on the large piston. As a result of which heavy load placed on larger piston is easily lifted upwards.
Pressure in fluids
1. Does Archimedes principle hold in a vessel in a free fall? [1]
Ans 01. Archimedes’s Principle will not hold in a vessel in free – fall as in this case, acceleration due to gravity is zero and hence buoyant force will not exist.
2. Why does not the pressure of atmosphere break windows? [2]
Ans 02. Pressure of atmosphere does not break windows as atmospheric Pressure is exerted on both sides of a window, so no net force is exerted on the window and hence uniform pressure does not break the window.
3. If a big drop of radius R is formed by 1000 small droplets of water, then find the radius of small drop?
[2]
4. A boulder is thrown into a deep lake. As it sinks deeper and deeper into water, does the buoyant force changes? [2]
Ans 04. The buoyant force does not change as the boulder sinks because the boulder displaces the same volume of water at any depth and because water is practically incompressible, its density is practically the same at all depth and hence the weight of water displaced or the buoyant force is same at all depths.
5. At what depth in an ocean will a tube of air have one – fourth volume it will have on reaching the surface? Given Atmospheric Pressure = 76 cm of Hg and density of Hg = 13.6g/cc? [2]
6. Why is it painful to walk barefooted on a road covered with pebbles having sharp edges? [2]
It is painful to walk bare – footed on a road covered with pebbles having sharp edges because they have small area and since: Pressure = force / Area, Area is less i.e. pressure is more.
It Means our feet exert greater pressure on pebbles and in turn pebbles exert equal reaction on the feet.
7. A liquid stands at the same level in the U – lube when at rest. If A is the area of cross section of tube and g is the acceleration due to gravity, what will be the difference in height of the liquid in the two limbs when the system is given acceleration ‘a’? [2]
8. Two balloons that have same weight and volume contains equal amounts of helium. One is rigid and other is free to expand as outside pressure decreases. When released, which balloon will rise higher? [2]
The balloon that is free to expand will displace more air as it rises than the balloon is rigid and restrained from expanding. Since the balloon is free to expand will experience more buoyant force and rises higher.
9. An object floats on water with 20% of its volume above the water time. What is the density of object? Given Density of water = 1000 kg|m3. [2]
10. A cubical block of iron 5cm on each side is floating on mercury in a vessel:-
1) What is the height of the block above mercury level?
2) Water is poured into vessel so that it just covers the iron block. What is the height of the water column?
Given Density of mercury = 13.6g|cm3 and Density of iron = 7.2 g|cm3