What happens when two objects of different masses fall freely near the surface of the moon starting from the same height which one will reach first and why?

Text Solution

have same velocity at any instanthave different accelerationexperience forces of same magnitudeundergo a change in their inertia

Answer : A

Solution : Two object of different masses falling freely near the surface of moon will have same velocities at any instant. This is because for both,`u=0,a=g,v=u+at=0+g t=g t=`same for both.

• 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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• 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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• 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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• 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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• 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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• 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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• Answer:

    (c) Law of gravitation is applicable to all bodies having some mass. And is given by

  
  where, F = Force of attraction between the two bodies
  
   = Mass of two bodies G = Gravitational constant r = Distance between the two bodies.
  

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• Answer:

    (d) G is the constant of proportionality and is called the universal gravitational constant. It is independent of mass and radius of the earth.
  

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• Answer:

    (b) We know that, according to gravitational force

  
  where,   F = Force between Two moss M = First moss m = Second mass G = Gravitational Constart r = Distant between Two mass According to the question, F ? = New force when mass is doubled If mass of each particle is doubled i.e.,                       M = 2 M and m = 2 m These value put in Eq, (i), we get
  
                            
  
                                 
  
  From Eq, (i),              
  
  
  

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• Answer:

    (a) The atmosphere is held to the earth by gravity.
  

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• Answer:

    (d) We know that, the gravitational force,

  
  
  Where, F = Force between mass m = Mass of the body M = Gravitational Constant r = 'Distant between two mass Given, M=1 unit, m=1 unit and r=1 unit, we get
  
  Therefore, the force of attraction between two unit point masses separated by a unit distance is called universal gravitational constant.
  

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• Answer:

    (a) The weight of an object, w = mg At the centre of the earth, acceleration due to gravity g is zero. And is given by

  
  where h = distance from surface of the earth to centre of the earth and at centre (h = R) i.e.,               g'= 0. So,                                         
  
  
  

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• Answer:

    (a) Given, Weight of an object in air =1 ON Weight of an object in water =8N So, the weight of the liquid displaced by the object F = 10 ? 8 = 2N and we know that according to Archimedes' Principle, buoyancy force = weight of the liquid displaced by the body.
  

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• Answer:

    (b) Now, according to question, when base is formed by breadth and width. Area will be minimum. And so, pressure will be maximum.
  

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• Answer:

    (d) According to Newton's universal law of gravitation, force exerted by the one body to other body is equal in magnitude and given by

  
  and opposite in direction.
  
   
  

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• Answer:

    The motion of the planet around the earth is due to the centripetal force. This centripetal force is provided by the gravitational force between the planet and the sun.

  
  This force depends on the mass of the sun and mass of the planet, and on the distance between sun and planet.
  

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• Answer:

    Time taken by both stone is given by second equation of motion

  
  As,                           
  
  so,
  
  and here                            s = h Where, m = Initial velocity in y-axis a = g acceleration due to gravity t = time displacement to time So,                            
  
                                 
  
  Therefore, if we drop down a stone from a height (h) and at same time throw another stone in horizontal direction, then both the stone strike the earth simultaneously at different places.
  

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• Answer:

    In the absence of gravity of earth, the moon flies off along a straight line. This straight line will be a tangent to the circular path.

  
  
  

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• Answer:

    No, those packets do not take same time to reach the surface of the earth. Because the value of g (i.e., acceleration due to gravity is) different at poles and equator due to rotation of the earth and is given by

  
   and at poles
  
  where as at equator
  
  . So, value of g at equator is less than value of g at poles and we know that.
  
  i.e.,
  
  Since, g is greatest at the poles than at the equator. So, packet dropped above the North Pole will reach first at the surface of the earth.
  

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• Answer:

    On earth Force applied by the man (F) on earth = m x g (m=mass) On moon

  
   so, by same force he can lift
  
  as
  
  so,
  
  
   As Mass does not change at every place. It is a concerned quantity. So, 15 kg will be maximum mass which can be lifted by the same force applied by the person on the moon.
  

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• Answer:

    We know that,

  
  , where M = Mass of the earth, R = Radius of the earth. So, mass of the earth,
  
                ...(i) If the earth is considered as a sphere of radius R and of material of density
  
  , then Mass of the earth = volume of the earth x density   [
  
   volume of sphere
  
   ]
  
   From Eq. (i), we get
  
  
              
  
   
  

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• Answer:

    The earth revolves around the sun. The centripetal force is needed by the earth to revolve around the sun. This centripetal force is provided by the gravitational force between the sun and the earth. And this gravitational force restricts the earth to fall into the sun,
  

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• Answer:

    Let radius and mass of the earth be R, M respectively and mass of an object be m. Weight of the object,

  
  ?.1
  
  According to the question, the diameter of the earth becomes half of its present value.  So, radius also becomes half of its initial values So,                         
  
  Again mass of radius also becomes half of its initial values So,                        
  
  Now, weight of the object                                
  
  Put
  
   and M' = 4 m in above formula, we get                                
  
                                 
  
                                 
  
  From Eq, (i). we get            w' = 16 w Thus, weight of the object wilt become 16 times of its original weight.
  

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• Answer:

    The force of attraction between two bodies of masses

  
  , and
  
  and separated by distance r is given by Newton's universal law of gravitation i.e.,
  
  where, G is the universal constant in nature. This force is known as gravitational force. The gravitational force is directly proportional to the product of the masses of two bodies and inversely proportional to the square of the distance between them. All bodies fall with the same acceleration due to gravity whatever their masses have. i.e.,
  
    (where M = Mass of the earth, R = Radius of the earth) and from the equation it is clear that, acceleration due to gravity (i.e., g) depends only on mass of the earth, the radius of the earth. So, two bricks tied together will not fall faster than a single bricks under the action of gravity. Hence, the hypothesis is not correct.
  

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Answer:

  From second equation of motion,                          

                 [for I object u=0] So,     

                where, h = Displacement, u = Initial velocity, t = Time and g = Acceleration due to gravity

                         

i.e.,                                

Time taken by first object of mass,

                               

  [for II object u=0] Similarly, time taken by object of mass

                               

(i) Acceleration due to gravity is independent of mass of falling body. So, the ratio remains the same. (ii) If bodies are hollow, then also ratio remains the same i.e.,

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Answer:

  (i) Buoyant force,

(where,

= Density of water, V = Volume of water displaced by the body) Buoyant force depends upon volume and density, since, saturated salt solution have higher density than the water. So, in saturated solution, cube will experience a greater buoyant force. If each side of the cube is reduced to 4 cm, then the volume of cube become less. As buoyant force is directly proportional to the volume. So, buoyant force will be less than as compared to the first case for water. (ii) The magnitude of the buoyant force given by

where V = Volume of body immersed in water or volume of water displaced,

 = Density of liquid. [

 Given, mass of a ball = 4 kg, density

]

Volume of solid

                               

Buoyancy,