Force - C. Science

New­tons Uni­ver­sal Law of Gravitation

Accord­ing to this law every object in the uni­verse attracts every other object with a force, which is directly pro­por­tional to the prod­uct of their masses and inversely pro­por­tional to the square of the dis­tance between their centres

Let us con­sider two bod­ies of masses   and  sep­a­rat­ed by a dis­tance ‘r’ as shown in fig. If ‘F’ is the force of attrac­tion between the two masses then accord­ing to Newton’s Law of grav­i­ta­tion

i) The force is directly pro­por­tional tothe prod­uct of masses   .….….….….(i)

ii) The force is inversely pro­por­tional to the square of the dis­tance between them  .….….….….(ii)

On com­bin­ing equa­tion ‘i’ and ‘ii’ we get

Here ‘G’ is a con­stant called uni­ver­sal grav­i­ta­tion con­stant. “G” is called uni­ver­sal grav­i­ta­tional con­stant because its value remains same through out the universe.

We know that (From Newton’s Uni­ver­sal Law)

If  = 1 kg,  = 1 kg and r=1m

The uni­ver­sal grav­i­ta­tional con­stant is the force of attraction between two masses of 1 kg each kept at a dis­tance of 1m.

Value of ‘G’ — Uni­ver­sal grav­i­ta­tional constant

Its value is 

The value of ‘G’ is very small, hence we can say that, it is the weak­est force in nature.

It is because of small value of ‘G’ that the force of grav­i­ta­tion between two small masses is negligibly small. It becomes appreciable only when at least one body is huge like planets, suns etc

Some impor­tant facts about grav­i­ta­tional force of attraction

1. The grav­i­ta­tion force does not change with change in the medium between the point masses.
2. It is the weak­est force in nature.
3. It is always attrac­tive in nature.
4. It obeys inverse square law. It means .
5. This force is a cen­tral force. This means that this force acts along the line join­ing the particles.
6. This force is a long range force. It is applic­a­ble between the galax­ies too.

Grav­ity :

Grav­ity is the force by which a planet, satel­lite or a star attracts an object on its sur­face or near it towards the cen­tre. It is denoted by the lett er ‘g”

Unit:  (SI)

Value:9.8 

Accel­er­a­tion due to grav­ity is  9.8 , it means that the veloc­ity of falling body increases by 9.8m/s every second.

Feather and coin experiment

It is the exper­i­men­tal proof that falls of objects do not depend on the mass of falling objects if air resis­tance is neglected. i.e. The accel­er­a­tion due to grav­ity of freely falling bod­ies is inde­pen­dent of their mass,if there is no air resistance.

Dif­fer­ence between grav­ity and Grav­i­ta­tional constant

grav­ity (g)	Grav­i­ta­tional con­stant (G)
i. Accel­er­a­tion of a body falling towards the earth’s sur­face    without any resis­tance is known as accel­er­a­tion due to gravity	i. G, the uni­ver­sal grav­i­ta­tional con­stant is the force of grav­i­ta­tion between two objects of unit masses placed unit dis­tance apart
ii. The value of g varies from place to place on earth surface.	ii. The value of G is constant
iii. The value of ‘g’ is  near the sur­face of the earth.	iii.The value of ‘G’ is
iv. It is a vec­tor quantity.	iv. It is a scalar quantity.

If object is at the height ‘h’  from the earth sur­face then its dis­tance from the cen­tre of the earth is ‘R+h’ . If accel­er­a­tion due to grav­ity at this height is g’ then we have  ; where M is mass of earth and G is grav­i­ta­tional constant.

If mass of the earth is M, radius is R, grav­i­ta­tional con­stant is G and accel­er­a­tion due to grav­ity at the earth sur­face is ‘g’ then we have 

NOTE:

• In the poles ‘g’ is max­i­mum, hence weight is also more.
• In equa­tor ‘g’ is min­i­mum so weight is less.
• If there is increase in alti­tude, ‘g’ decreases, hence weight also decreases
• If there is increase in depth, ‘g’ decreases there­fore weight aslo decreases and at cen­ter of earth g = 0 , there fore weight is zero
• The grav­ity of moon is 6 times less than that of earth.
• Mass:The quan­tity of mat­ter con­tained in a body is called its mass.
  Unit: Kg (SI)
  The mass of a body remains same at all places. The mass of a body can be mea­sured with the help of a pan balance.
  Weight:
  The weight of a body on the earth is equal to the force with which the body is attracted towards the  cen­tre of the earth.
  Unit: New­ton (N)
  Weight is a vec­tor quan­tity. Weight is mea­sured by a spring bal­ance. The weight of the body is the  prod­uct of its mass and accel­er­a­tion due to grav­ity hence the weight of a body is not same every­where on the earth.
  
  
  W = mass (m) * accel­er­a­tion due to grav­ity (g)
  
  

  Dif­fer­ence between Mass and Weight

  Mass	Weight
  i. The quan­tity of mat­ter con­tained in a body is called its mass	i. Weight of a body on earth is qual to the force with which the body is attracted towards the earth.
  ii. It is a scalar quantity.	ii. It is a vec­tor quantity
  iii. The unit of mass is kg in SI system.	iii. The unit of weight is New­ton in SI system
  iv. It is a fun­da­men­tal quan­tity which remains same every­where .	iv. It is a derived quantity.
  v. It can be mea­sured by pan balance.	v. It can be mea­sured by spring balance.

  
  

  Freefall:

  If an object is falling with the accel­er­a­tion of accel­er­a­tion due to grav­ity in the absence of air resis­tance is called free fall.
  
  

  Weight­less­ness:

  The weight of an object falling freely under grav­ity appears to be zero. This con­di­tion is called weightlessness.
• 
  
• Other Important Questions
• 1. Is the falling of  “Para­chute” on the earth’s sur­face free fall?

  Ans: No, the falling of Para­chute on the earth’s sur­face is not free fall because it has larger sur­face area due to which it offers the larger air resis­tance which decreases the accel­er­a­tion of the para­chute so, the para­chute will fall towards the earth’s sur­face approx­i­mately with con­stant velocity.

  2. Why does a per­son in space­craft feels weightlessness?

  Ans: Dur­ing the orbit of space­craft on the earth, the direc­tion of cir­cu­lar motion of space­craft gets changed at every point i.e. it gets accel­er­ated. So, direc­tion of accel­er­a­tion is towards the cen­tre of rota­tion. The cen­tripetal force helps the space­craft to move in a cir­cu­lar path which is pro­vided by grav­i­ta­tional force of earth. So, the astro­naut and space­craft are in con­tin­u­ous state of free fall. There exists no force between space­craft and astro­naut. This gives the impres­sion of freefall and the per­son inside space­craft feels weightlessness.

  3. At what con­di­tion does the body hav­ing fixed mass have zero weight?

  i. When the body falls freely under the action of gravity.

  ii. When the body is in outer space away from the earth’s grav­i­ta­tional field where the force of grav­ity is zero

  4.  Weight of body is more in polar region than in equa­to­r­ial region of the earth. Why?

  As we know . The value of grav­ity ‘g’ is more at poles than at equa­tor i.e  as radius is less at poles com­pared to equa­tor.  Hence, weight of a body is greater at pole than  at the equator.

  5. In real life, objects have no com­plete freefall?

  In real life, objects have no com­plete freefall because there is always the pres­ence of air resis­tance in this world.

  6. Weight of body is less on the moon than on the earth. Why?

  Weight of body is directly pro­por­tional to g (i.e.  ) . The ‘g’ of earth is 6 times greater than that of moon. Thus the weight of body is less on the moon than on the earth.

  7. G is called uni­ver­sal grav­i­ta­tional con­stant, Why?

  G is called uni­ver­sal grav­i­ta­tional con­stant because the vale of G remains con­stant every­where ie.  and it is not affected by any medium i.e. air, water etc.

  8. Newton’s law of grav­i­ta­tion is called uni­ver­sal law. Why

  Newton’s law of grav­i­ta­tion is called uni­ver­sal law because it is applied for any object that may be very small (micro ) objects as well as very large (macro) objects.

  9. It safe when jumped from aero­plane with the help of parachute?

  The para­chute has more air resis­tance due to its large shape and size. After falling cer­tain dis­tance, the upward force of air resis­tance equals to the down­ward force of grav­ity and a man with para­chute falls with uni­form veloc­ity. Thus, it is safe when jumped from aero­plane with the help of parachute.

  10. Among moon, earth and Jupiter, which one will have more grav­ity and why?

  Among moon, the earth and Jupiter, JUPITER will have more grav­ity because grav­ity of planet depends upon mass (i.e.  ). Since the Jupiter has more mass than earth and moon its grav­ity is more.

  11. What is grav­i­ta­tional field intensity?

  The grav­ity that applies to an object of unit mass present on the sur­face of the planet or satel­lite, is known as grav­i­ta­tional field inten­sity of a planet.

  12. An iron ball and feather are dropped simul­ta­ne­ously from the same height in vac­cum which one will strike the ground first and why?

  An iron ball as well as feather both will strike the ground at the same time with the same accel­er­a­tion because in the absence of air resis­tance in vac­uum both the bod­ies falls freely on the ground. Thus both bod­ies irre­spec­tive to their masses fall at the same time.

  13. If a body is dropped from same height in an equa­tor and pole from which place the body will reach the ground faster?

  The body will reach the ground faster from the poles because the value of g at poles is greater than the value of g at equa­tor. So, more the value of g, less will be the time taken by a body to fall from the pole.

  14. One can jump higher on the sur­face of the moon than on the earth sur­face, why?

  Since we know that accel­er­a­tion due to grav­ity of planet depends upon the mass of the planet. In com­par­i­son to earth, moon has less grav­ity because mass of moon is less than the mass of the earth. So, one can jump higher on the sur­face of the moon than on the earth sur­face.

  15. The accel­er­a­tion due to grav­ity in the earth is  . What does it mean?

  The accel­er­a­tion due to grav­ity in the earth is   it means the veloc­ity of the body increases at the rate of 9.8m/s.

  16. It is dif­fi­cult to lift a large stone on the sur­face of the earth but easy to lift small one. Why?

  It is so because large stone has more force of attrac­tion of the earth as it has more mass (i.e. F = mg) But, the smaller one has less force of attrac­tion as it has less mass. So, it is eas­ier to lift small stone than large stone.

   17. Why the weight of a body decrease with increase in dis­tance from the cen­tre of the earth?

  The weight of a body decrease with increase in dis­tance from the cen­tre of the earth because weight is inversely pro­por­tional to the square of the dis­tance i.e.  . Hence, weight depends upon dis­tance between two bod­ies. i.e. earth and the object)

  18. What is the con­clu­sion of feather and coin experiment?

  Accel­er­a­tion due to grav­ity doesn’t depend upon the mass of the body. More the sur­face area of the body, more will be the air resis­tance which decreases accel­er­a­tion due to gravity.

  19. There is no use of para­chute on the moon. Why?

  The para­chute falls freely with accel­er­a­tion due to grav­ity on the moon due to absence of air resis­tance as there is no atmos­phere. Hence there is no use of para­chute on the moon.

  20. Weight of the body at the cen­tre of the earth is zero. Why

  Since the value of accel­er­a­tion due to grav­ity is zero at the cen­tre of the earth, the weight of a body is zero at the cen­tre of the earth.