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    • Law of gravitation
    • Acceleration(g)
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    • Numerical Problems
  • Heat
    • Heat Energy
    • Anomalous expansion of water
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  • Wave Motion

Upthrust

Definition:The resultant force applied by the liquid on substance when substance put on liquid is called upthrust. Its unit is (Newton) N . By the formula, Upthrust = w1 − w2 where, w1 is the weight of subtance in air and w2 is weight of the substance in medium

→ Upthrust given by the liquid is directly proportional to density of liquid i.e. as the density increases upthrust increases and vice versa. The substance having lower density than liquid floats on liquid. The substance having higher density than liquid sinks in liquid. To floats on liquid, substance should displace liquid of weight at least equal to its weight.

Points to be noted
1. → Density of iceberg is less than the water so iceberg floats in water.
2. → Density of dead body is less than water but head is more denser so a dead body floats with its head immersing in water.
3. → Egg density is more than water so it sink in pure water but Egg has less density than salty water so it floats on salty water.
4. → Having higher density salty water give more upthrust than pure river water so it is easire for a man to swim in sea water than in river water.
5. → Water give upthrust on stone when put in it so it is easier to lift a heavy stone inside the water.
6. → Density of iron nail has high than water but have low density than mercury so iron nail sink in water and floats in mercury
7. → Iron has high density than water. Iron nail couldn't displace water at least equal to its weight but ship of wider base can displace water equal to its weight so nail sinks and ship floats.
   Q. Prove that : When an object float on water then upthrust given by water is equal to weight of object.
   →

   Suppose an object ABCD of base area A. Whose side AB is at depth h1 and side CD is at depth h 2. If density of water is 'd' and gravitaitonal acceleration 'g', then pressure on surface AB is P 1 = h 1d g. Force on surface AB is F 1 = A P 1 = A h 1d g Pressure on surface CD is P 2 = h 2 d g. Force on surface CD is F 2 =A P2 = A h 2 d g Resultant force on object is F = F 2 - F 1 or Upthrust = A h 2 d g - A h 1d g = A d g ( h 2 - h 1) = V d g = mg ∴ Upthrust = weight of object (w = mg)

Do yourself
• Q. During dipping out of water from a well, it is easier to lift the bucket while it is still inside water than it is out of water. Why?
• Q. Prove that: Upthrust = Adg(h₂ − h₁
• Q. Prove that : Upthrust = Vdg
• Q. It is easier to swim with wearing life jacke, why?
• Q. What is the difference between floating emptly boat and full with goods boat?
• Q. It is easier to move hand in water than air, why?
• Q. Hydrometer sinks more in Kerosen than in water, why?
• Q. How much weight of floating object in water?
  → The weight of floating object in water is zero because force of gravity is balanced by upthrust.
• Q. In a city drinking water tank is placed at higher place, why?
  → As water tank is placed at high, it generate high pressure so that it is possible to distribute water wide area and uniformly.
• Q. Atmospheric pressure is more in terai than in Himal, why?
• Q. As we go at very high place it may overflow blood from ear, nose, eye etc. why?
  → Because of low atmospheric pressure at high level than blood pressure inside body, it may overflow blood from ear, nose, eye etc.
• Q. In aeroplane, why not allowed to founten pen, ball pen ?
  → Because of low atmospheric pressure at high level which may cause overflow of ink. So founten pen ball pen not allowed.
• Q. Watership can carry more load than airship, why?
  → Because of high upthrust of water than airwater ship can carry more load than airship

Q.Three matters and their corresponding densities are given
Question/Answer	Matter	Density
If we take equal volume of all three matters then Z is of least mass because of minimum density. If we take equal mass of all three matters then X is of least volume because of maximum density. Matter 'z' floats on water because of less density than water.	X	11 $\frac{\mathrm{gm}}{\mathrm{cm<sup>3</sup>}}$
	Y	8 $\frac{\mathrm{gm}}{\mathrm{cm<sup>3</sup>}}$
	Y	0.9 $\frac{\mathrm{gm}}{\mathrm{cm<sup>3</sup>}}$

Q. A stone is weighted in air, water and saltywater. Result is given on table.
Question/Answer	Medium	Weight
Medium A is salty water, B is air, C is water. Water displace by stone is 18 - 16 = 2 N (In kg it is $\frac{2}{\mathrm{10}}$= 0.2 kg. Mass of stone is m = $\frac{w}{\mathrm{10}}$= 18/10 =1.8 kg.	A	15 N
	B	18 N
	C	16 N