*__***GRAVITATION**

**UNIVERSAL lAW OF GRAVITATION**

A B

**M** **m**

I I

I I

I I

<---—R---——>

F momentum Mm —> F=GMm/R^{2} —>F momentum Mm/R^{2}

**F momentum 1/R**^{2}

—>G=FR^{2}/Mm = Nm^{2}/kg^{2} = N.m^{2}kg^{-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/R**^{2}

Unit of G=Unit Gv. Constt.

—>G=FR^{2}/Mm=Nm^{2}/kg^{2} = N.m^{2}kg^{-2}

**G=6.7*10**^{-11}Nm^{2}kg^{-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/R^{2} > GMm/(2R)^{2}

GMm/R^{2} > GMm/(4R^{2})

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/R^{2}(II)

from (I) and (II)

Since LHS=F

mg=GMm/R^{2}

g=GM/R^{2}

**Example:-**

g=6.7*10 Nm^{2}/kg^{2}*6*10 kg/(6.4*10^{6}m)^{2}

g=(6.7*6)*(10^{-!!}*10^{24})Nm^{2}kg/kg^{2}*6.4*6.4*10^{6}*10^{6}m^{2}

g=40.2*10^{13}kg m / kg*40.96*10^{2} s ^{2}

=40.2/40.96*10m/s^{2}

**=9.8m/s**^{2}

**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

>We=Gm Me/Re^{2}(I)

>Wm=Gm Mm/Rm^{2}(II)

Divide (I) by (II), we get

We/Wm=Gm Me/Re^{2} * Rm^{2}/GMm^{m}=(Me)/(Mm)(Rm)^{2}/(Re)

We/Wm=(5.98*10kg^{24})/(7.36*10^{22}kg)*(1.74*10^{6}m)/(6.4*10^{6}m)

=(0.8125*10^{2})(0.273)^{2}

We/Wm=(0.8125*10^{2})(0.075)

=0.060*10^{2}=6—>**Wm=1/6We**