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Bernoulli's theorem is based on :
Conceptual
Two spherical soap bubbles of radii r1 and r2 in vaccum collapse under isothermal condition. The resulting bubble has radius equal to :
The energy needed in breaking of a drop of liquid of radius R into n drops of radius r is given by (T is surface tension and P is atmospheric pressure) :
A rectangular film of liquid is extended from (4 cm) to . If the work done is J,the value of the surface tension of the liquid is
(b) Increases in surface energy= work done in areaSurface tension
Increase in surface area,
=
So, work done, W=T.
Three liquids of densities (with ), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact obey
(b) According to ascent formula for capillary tube,
Two non-mixing liquids of densities and n(n>1) are put in a container. The height of each liquid is h. A solid cylinder floats with its axis vertical and length pL in the denser liquid. The density of the cylinder is d. The cylinder floats with its axis vertical and length pL (p<1) in the denser liquid. The density d is equal to
The approximate depth of an ocean is 2700 m. The compressibility of water is 45.4 x 10-11 Pa-1 and density of water is 103kg/m3. What fractional compression of water will be obtained at the bottom of the ocean?
Given d=2700 m
ρ=103kg/m3
Compressibility=45.4 x 10-11 Pa-1 per pascal
The pressure at the bottom of ocean is given by
P=ρgd=103x10x2700=27x106Pa
So, fractional compression=compressibility x pressure
=45.4 x 10-11x 27 x106
=1.2x10-2
A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is 250 m2. Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be (Pair=1.2kg/m3)
From Bernoulli's theorem
p1+ρv12=p2+ρv22
where, p1 and p2 are pressure inside and outside the roof and v1 v2 are velocities of wind inside and outside the roof, Neglect the width of the roof.
Pressure difference is
p1-p2=ρ(v22-v12)
=x1.2(402-0)=960N/m2
Force acting on the roof is given by
F=(p1-p2)A=960 x 250=24x104N=24X105N
As the pressure inside the roof is more than outside to it. So the force will act m the upward direction, i.e. F=24x105N,upward
The cylindrical tube of a spray pump has radius R, one end of which has n fine holes, each of radius r. If the speed of the liquid in the tube is v, the speed of the ejection of the liquid through the holes is
The heart of a man pumps 5L of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be kg/m3 and g =10 m/s2, then the power of heart in watt is
Given pressure=150mm of Hg
Pumping rate of heart of a man== m3/s
Power of heart=P.=ρgh. [P=ρgh]
=>(13.6x103kg/m3) (10x0.15x5x10-3)/60
=1.70W
Water rises to a height h in capillary tube . If the length of capillary tube is above the surface of water is made less than h, then
In case of insufficient length, angle of contact adjusts itself so that water does not spill
A certain number of spherical drops of a liquid of radius r coalesce to form a single drop of radius R and volume V. If T is the surface tension of the liquid, then
The wettability of a surface by a liquid depends primarily on
(d) The value of angle of contact determines whether a liquid will spread on the surface
An engine pumps water continuously through a hose. Water leaves the hose with a velocity v and m is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?
Let m is the mass per unit length then rate of mass per sec=
Rate of KE=
Two bodies are in equilibrium when suspended in water from the arms of a balance. The mass of one body is 36 g and its density is 9 g / cm3. If the mass of the other is 48 g, its density in g / cm3 is
(c) Apparent weight =
where m = mass of the body,
= density of the body
= density of water
If two bodies are in equilibrium then their apparent weight must be equal.
By solving we get