_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