Gravitation

_GRAVITATION

UNIVERSAL lAW OF GRAVITATION

A B
M m
I I
I I
I I
<-—R-——>
F momentum Mm —> F=GMm/R2 —>F momentum Mm/R2

F momentum 1/R2

—>G=FR2/Mm = Nm2/kg2 = N.m2kg-2

F=Force of attraction between A and B
R=Distance between Centre of A and B

M and m= Masses of body A and B
According to the Newton F Momentum Mm
F is directly propotional to product of masses F momentum Mm

F is inversely proptional to the square of distance between them
F=GMm/R2
Unit of G=Unit Gv. Constt.
—>G=FR2/Mm=Nm2/kg2 = N.m2kg-2

G=6.7*10-11Nm2kg-2
From the above we can say that
a)If the masses between them increases the force will also be increases.
b)If the distance between them decrease than force increases.

p=m*v
=kg m/s

example:-
GMm/R2 > GMm/(2R)2
GMm/R2 > GMm/(4R2)

Derivation of value G (Accerelation due to gravity)
Let M be the mass of Earth
R radius of the Earth
According to N second law of motion we have F=ma-(I)
or F=m*g
Where
F=force of attraction between A and B and g is the acceleration due to gravity
Also according to universal law of gravitation we have
F=GMm/(R+n)2—(II)
Since h«R
F=GMm/R2(II)
from (I) and (II)
Since LHS=F
mg=GMm/R2
g=GM/R2

Example:-
g=6.7*10 Nm2/kg2*6*10 kg/(6.4*106m)2
g=(6.7*6)*(10-!!*1024)Nm2kg/kg2*6.4*6.4*106*106m2
g=40.2*1013kg m / kg*40.96*102 s 2
=40.2/40.96*10m/s2
=9.8m/s2

MAss and Weight
Mass:-Mass is the measure of quantity of matter contained in a body. It is a scaler quantity thet remains constant irrespective of the location of the body.Thus, mass of the body on the Earth and the moon remains the same.
Weight:-Weight is the force with which a body (mass) a pulled towards the centre of the Earth or any other body like the sun , the moon , planets etc. It is a vector quantity. It depends on the force of gravity generated by a body while attracting another body.

Weight of an objecton the moon
Let:-
m=mass of object
We=Weight of the object on Earth
Wm= Weight of object on the moon
Re=radius of the earth
Rm=Radius of the moon
Me=Mass of earth
Mm=mass of moon

Divide (I) by (II), we get
We/Wm=Gm Me/Re2 * Rm2/GMmm=(Me)/(Mm)(Rm)2/(Re)
We/Wm=(5.98*10kg24)/(7.36*1022kg)*(1.74*106m)/(6.4*106m)
=(0.8125*102)(0.273)2
We/Wm=(0.8125*102)(0.075)
=0.060*102=6—>Wm=1/6We

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