What happens to the gravitational force between two objects if the mass of the one object is doubled and the distance between them is also doubled?

• Answer:

                  From the relationship,

  
    (i) If the mass of one object (say body 1) is doubled, then
  
    Thus, the gravitational force between the two objects gets doubled.   (ii) If the distance between the two objects is doubled, then
  
    Thus, the gravitational force between the two objects becomes one-fourth. If the distance between the two objects is tripled, then
  
    Thus, the gravitational force between the two objects becomes one-ninth.   (iii) If the masses of both the objects are doubled, then
  
    Thus, the gravitational force between the two objects becomes 4 times.  
  

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Page 2

• Answer:

  Universal law of gravitation is important as it accounts, (a) for the existence of the solar system, i.e., motion of planets around the sun. (b) for holding the atmosphere near the surface of the earth. (c) for the flow of water in rivers. (d) for rainfall and snowfall. (e) for occurrence of tides.  
  

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Page 3

• Answer:

  All objects moving towards earth on account of gravitational force of earth on them are said to be in free fall. This force produces a uniform acceleration in the object. This is acceleration of free fall and its value is 9.8 ms-2  .
  

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Page 4

• Answer:

  The gravitational force between the earth and an object is called the force of gravity or simply earth’s gravity.
  

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Page 5

• Answer:

  We know that the value of g is greater at the poles than at the equator. So the weight of gold at the equator will be less than the weight of gold at the poles. So it is obvious that the friend at equator will not agree with the weight of gold bought at poles.
  

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Page 6

• Answer:

  The sheet of paper falls slower than one that is crumpled into a ball because in first case the area of the sheet is more so it experiences large opposing force due to air. While the sheet crumpled into a ball experience less opposing force due to small area. 
  

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Page 7

• Answer:

  Here, m = 10 kg Mass is the same on earth and moon. Now, weight of the object on earth

  
  Weight of the object on moon,
  
   
  

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Page 8

• Answer:

  Initial velocity, u = 49 m/s Acceleration, a = g = - 9.8 m/s2 Velocity at the highest point, v = 0 m/s (i) If h is the maximum height reached by the ball, then

  
  or
  
  
    Thus, the ball will reach a height of 122.5 m. We have,
  
  Here,
  
  
  Total time
  
   
  

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Page 9

• Answer:

                  Initial velocity,

  
  Final velocity,
  
  Height of the tower,
  
  Acceleration due to gravity,
  
  Using the equation,
  
  
   
  

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Page 10

• Answer:

  Here,

  
  From
  
  
                          or           
  
    As final position of the stone coincides with its initial position, net displacement = 0 Total distance covered by the stone
  
   
  

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Page 11

• Answer:

  Mass of the earth,

  
   Mass of the sun,
  
    Distance between the earth and the sun,
  
    Then, the gravitational force between the earth and the sun is given by,
  
  
    Thus, the earth and the sun attract each other by a gravitational force of
  
   
  

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Page 12

• Answer:

  Here, h = 100 m. Let the two stones meet after t seconds at a point P which is at a height x above the ground as shown in figure.For stone 1,

  
  
                                    
  
  From
  
  
                                 .....(i)                 For stone 2,
  
                                                             From
  
  
                           ......(ii)   Adding equations (i) and (ii)
  
  
     
  

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Page 13

• Answer:

                  Here, time of ascent = time of descent,

  
  (a)
  
  From
  
  
    (b) From
  
  
    (c)
  
   ball is at maximum height. From
  
  
  (below the top)  
  

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Page 14

• Answer:

  When the object has density less than 1 g cm-1  then it floats on the surface of water, because, it always displaces more weight of water than its own weight. As buoyant force is more than its own weight, therefore, it floats. When the object has density more than 1 g cm-3   then it sinks in water, because it always displaces less weight of water than its own weight. As buoyant force is less than its own weight, therefore, it sinks.  
  

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Page 15

• Answer:

  In fact, a weighing machine is a sort of spring balance which measure the weight (and not the mass) of a body. When we stand on the weighing machine, our weight (which is due to gravitational attraction of the earth) acts vertically downwards. But the buoyancy due to air on our body acts vertically upwards. As a result of this, our apparent weight (true weight buoyant force) is less than the true weight Since the weighing machine measures the apparent weight, our true weight is more, i.e., more than 42 kg.    
  

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Page 16

• Answer:

  We know that true weight = apparent weight + up thrust. The cotton bag is heavier than the iron bar. This is due to the reason, that the bag of cotton which has more volume (as it has less density) than the iron bar (which has more density), experiences more up thrust due to air.
  

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Page 17

• Answer:

  If an object is immersed in a liquid then the buoyant force due to liquid acts on the object in vertically upward direction.
  

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Page 18

• Answer:

  The buoyant force acting on the block of plastic is more than its weight. As a result of this, it comes up when released under water. The cause of this larger buoyant force on the block of plastic is due to its density being smaller than that of water.
  

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Page 19

• Answer:

  Density of water

  
  Mass of substance
  
  Volume of substance
  
  
  Density of substance
  
    As the density of the substance is greater than that of water, the given substance will sink in water.  
  

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Page 20

• Answer:

  Here, mass of packet, M = 500 g volume of the packet, V = 350 cm3 Clearly, density of packet,

  
    Since the density of packet is more than density of water, the packet will sink. As the packet is fully submerged in water, mass of water displaced by the packet = volume of the packet x density of water        = (350 cm3) x (1 g/cm3) = 350 g    
  

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Page 21

• Answer:

  (d) Objects of different masses falling freely near the surface of the moon would have the same velocities at any instant because they will have same acceleration due to gravity.
  

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Page 22

• Answer:

    (c) It is least at the equator and maximum at the poles due to rotation of earth                                       i.e., it is given by  

  
  
  At poles
  
  , So g maximum     At equator
  
  , So g maximum       
  

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Page 23

• Answer:

    (a) We know that, according to force of gravitation

  
   (G= Gravitational constant) where
  
   and
  
  are the masses of two objects respectively. And r is the distance between the two masses Now, according to the question, if masses of both objects are halved, i.e.,                       
  
   and
  
  New force   
  
                                 
  
  where
  
   So, new force
  
             Thus, the new gravitational force will become
  
   times of its original gravitational force.
  

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Page 24

• Answer:

    (c) In circular motion, the direction of velocity at a point is always along the tangent at that point. If string breaks, then the centripetal force acting on the stone becomes zero and it will move along a straight line tangential to the circular path.

  
  where
  
   are the velocities point A, B, C, D in circular path.
  

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Page 25

• Answer:

    (d) In a liquid of higher density more part of the object remains outside the liquid. Since, the order of part of their volume outside the liquid is given by (part of the body outside the liquid) a- densities of liquid

  
  Thus, the order of densities in increasing order is
  
  
  

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Page 26

• Answer:

    (d) The quantity G is universal constant of nature. It is applied to all the body present in universe It is constant of proportionality in Newton's universal law of gravitation. The accepted value of G is

  
  
  

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