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• Gravitational Force: A force through which all objects attract each.
• Universal Law of Gravitation: Two objects attract with force which is directly proportional to product of masses and inversely proportional to square of distance between them.
• Mathematical expression of universal law of gravitation:
  • F = G (M × m ) / d², where G is gravitational constant
  • Numerical value for G = 6.673 × 10^-11 Nm²/ kg²
  • SI unit of G: Nm²/ kg²
• Significance of Universal Law of Gravitation- Free fall:
  • Body falling towards the earth undergoes change in velocity. This shows that body possess acceleration. This acceleration is result of gravitational force acting on body known as acceleration due to gravity.
  • Mathematical expression of acceleration due to gravity: g = GM / d²Where, M = mass of earth, d = distance between object and earth.
  • Numerical value for acceleration due to gravity:g= 9.8 m/s²
  • If object is near the earth’s surface then distance between object and the earth is same as the radius of earth R g = GM / R²
  • Motion of object under influence of gravitational force of earth: When objects undergo free fall they face opposition of air and hence, take different time to reach the ground. But in vacuum objects reach on ground at the same time.
  • Equation of motion in terms of acceleration due to gravity:v = u + gt

    s= ut + ½ gt²

    v² = u² + 2gs

    g is positive, when acceleration is in direction of velocity.

    g is negative, when acceleration is opposite to direction of velocity.

• Mass: Quantity which depends on amount of matter and is constant at any place.
• Weight: Result of gravitational force acting on the body which acts in vertically downward direction and varies from place to place.
  • Weight (w) = Mass(m) × Acceleration due to gravity(g)
  • SI unit: Newton (N)
  • Weight on Moon: Weight of object on moon is result of gravitational force exerted by moon. As size of moon is small, gravitational force exerted by moon is less as compared to earth. Weight of object on moon is ⅙ weight of object on earth.

  Click here to watch video on Mass and Weight

• Comparison between mass and weight:
  

  Mass	Weight
  Depends on quantity of matter present in the body	Depends on gravitational force acting on body
  Constant at any place	Varies from place to place
  It is a scalar quantity	It is a vector quantity
  It is never zero	Can be zero in absence of gravity

• Thrust: Total force acting on the object perpendicular to surface.
• Pressure:
  • Thrust applied per unit area
  • SI unit: N/m² or Pascal (Pa)
  • In fluids pressure is exerted on the walls of container or in all direction. [Fluids can be liquid or gas]
• Buoyancy: Body when partially or completely immersed in liquid experience an upward force called buoyant force or upthrust. Magnitude of buoyant force depends on density of liquid.
• Floating and Sinking of Objects:
  • Objects having the density less than liquid, floats on liquids
  • Object having the density more than liquid, sinks in liquids
  • E.g: Nail have density more than water, hence, it sinks. Cork has density less than water, hence, it floats.
• Archimedes principle: Object when partially or completely immersed in liquid, displaces amount of liquid equal upthrust of fluid. E.g: If an object weighing 100 grams is immersed in container of water, the amount of water displaced will be 100 grams.
• Application of archimedes principle:
  • Used for designing of ships and submarines
  • Hydrometers : It identify density of liquids
  • Lactometers : To detect purity of milk
  • For controlling hot air balloon
• Density: Mass per unit volume.
• Relative density: Ratio of density of substance to density of water.