Gravitation- Class IX

Q According to Universal law of gravitation- every body on the earth attracts every other body with a gravitational force, why then this force does not cause any motion in the objects?
Ans Though the various objects on this earth constantly attract each other, they do not cause any motion because-
1) Each body experiences multiple forces from different directions and most of these forces get cancelled from each other.
2) The gravitational force of attraction between them is very small due to their comparatively small masses.

Gravitation and Newton's laws of motion

According to Third law of motion every action has equal and opposite reaction. This means that if earth attracts a body towards it witha force,F then the body also attracts earth with same force but in opposite direction i.e. -F. But we know that earth does not move towards the object because according to second law of motion, F=ma

a=F/m

As we see that acceleration is inversely proportional to m, therefore a negligible acceleration is produced in earth due to its high mass.

Acceleration due to gravity

If we drop a body of mass 'm' from a distance 'R' from centre of earth of mass 'M', then earth will exert a force of gravitation on the body,F

F=G M m/R*R - 1

According to second law of motion, F=ma -2

Equating 1 and 2

GMm/R*R = ma

a= GM/R*R

Since we know that in case of free fall, a= g (acceleration due to gravity),

g= GM/R*R

Putting values, we get g=9.8 m/s*s

Dependence of acceleration due to gravity

1) Since acceleration due to gravity is independent of mass of object i.e. 'm', therefore, both light and heavy objects are accelerated by same amount.

2) As 'g' depends on 'R', the value of 'g' varies at poles and equator. Since, 'R' is more at equator, 'g' is small at equator and 'R' is less at poles, therefore, 'g' is more at poles.

Weight on moon

Let We= weight on earth and Wm= weight on moon

Wm= GM*m/R*R where M is mass of moon, m is mass of object and R is radius of moon

Now, mass of earth is 100 times mass of moon and radius of earth is 4 times radius of moon

We= G 100M*m/4R*4R

We= 100GmM/16R*R

Wm/We= 16/100

or approximately, Wm/We=1/6

Therefore, weight of an object on moon is 1/6th of weight of that object on earth.

Difference between mass and weight
Mass
1) The mass of an object is the quantity of matter contained in it.
2) The S.I. unit of mass is kilogram (kg).
3) The mass of an object is constant.
4) The mass of an object can never be zero.

Weight
1) The weight of an object is the force with which it is attracted towards the centre of the earth.
2) The S.I. unit of weight is Newton (N).
3) The weight of an object is not constant. It changes with the change in acceleration due to gravity (g).
4) The weight of an object can be zero. e.g. in the interplanetary space, where g=0, the weight of an object becomes zero.

Equations of motions for freely falling bodies

1) v=u+gt

2) h=ut+ 1/2gt*t

3) v*v= u*u+ 2gh

IMPORTANT POINTS TO REMEMBER

1) The physical quantities having vertically upward motion are assigned +ve values whereas the physical quantities having downward motion are assigned -ve values.

2) The acceleration due to gravity of earth is always taken -ve.

3) When a body is dropped freely from a height, its initial velocity 'u' is zero.

4) When a body is thrown vertically upwards, its final velocity 'v' becomes zero.

5) The time taken by a body to rise to the highest point is equal to the time it takes to fall from the same height.