ROTATION OF 2 MASSES UNDER MUTUAL Variation
NEWTON‛S LAW OF VARIATION IN THE VALUE OF
GRAVITATION GRAVITATIONAL FORCE OF ATTRACTION
ACCELERATION DUE TO GRAVITY
m1 F F m2 Gm22
r V1 = Variation due to height ‘h‛
(m1+m2) r
Gm1m2 m g
v2 GM mg
F = g =
r 2
V2 =
Gm12
h (R + h)2
G - Universal gravitational constant (m1+m2) r g gR2
Value of G r1 COM r2 r g =
6.67x10-11 Nm2Kg-2 (SI or MKS) v1
r 3
(R + h)2
T2 = 4 2
6.67x10-8 dyne cm2g-2 (CGS) r G(m1+m2) Re
General Equation
Time period M Note = value
Dimensional formula [G] Approximate equation
or T2 r3 For poles
M-1L3T-2 h<<<<<<R (h < 100 km)
There is no e
2h earth on the
use, gl= g 1-
R For equator
IMPORTANT POINTS ABOUT Note the point
THREE MASSES(EQUAL) REVOLVING The effect o
GRAVITATIONAL FORCE If h<<<<R, then decrease in the value
UNDER MUTUAL GRAVITATIONAL FORCE the value of
1. Gravitational force of g with height
V M When a body
*Always attractive in nature 2hg the poles, we
GM GM Absolute decrease = g = g - gl =
R
*Independent of the nature of medium V1 = = m (gp - g
l R 3 g g-gl 2h
between masses and presence or absence of Fractional decrease = = =
l l g g R
other bodies R
g g-gl 2h x 100
2. Are central forces, acts along the centre c Time period Percentage decrease = = x 100 =
V g g R ORBITAL V
of gravity of two bodies. M
T2 l3 Orbit at a he
3. Conservative force V
l M
Variation due to depth ‘d‛ m,V
4. Force between any two masses - h
g
Gravitational force
r
d gl = g [ 1- d
] Re
Force between earth and any other body - R g
l R
M
r
Force of gravity
M Re
FOUR EQUAL MASSES UNDER MUTUAL
GRAVITATIONAL FORCE If orbit is cl
earth‛s surfa
g dg
= g-g =
l
l GM Absolute decrease = (called minimum
V = (2 2+1) g R
VECTOR FORM 2 2l Note - for e
F21 force on 2 due to 1 g g-g l
d
y
l l 1 GM Fractional decrease = = = gR = 8 km
r12 vector from m1 to m2 V = g g R
R (2 2+1)
r12
G m1m2 2 R d
m2
-r12 l Percentage decrease = g x100
GM
m1
F21 = x100 = or = 6
r2 r122 l
T2 l3 Here R = g R R
r1 2
Very imp graph
G m1m2
x or - r12 The graphical representation of change in KE, PE OR T
r123
Similarly the value of g‛ with height and depth SATELLITE
F12 force on 1 due to 2 GRAVITY gl
GMm
Acceleration due to gravity GMe KE =
G m1m2 G m1m2 2r
NEWTON‛S LAW OF VARIATION IN THE VALUE OF
GRAVITATION GRAVITATIONAL FORCE OF ATTRACTION
ACCELERATION DUE TO GRAVITY
m1 F F m2 Gm22
r V1 = Variation due to height ‘h‛
(m1+m2) r
Gm1m2 m g
v2 GM mg
F = g =
r 2
V2 =
Gm12
h (R + h)2
G - Universal gravitational constant (m1+m2) r g gR2
Value of G r1 COM r2 r g =
6.67x10-11 Nm2Kg-2 (SI or MKS) v1
r 3
(R + h)2
T2 = 4 2
6.67x10-8 dyne cm2g-2 (CGS) r G(m1+m2) Re
General Equation
Time period M Note = value
Dimensional formula [G] Approximate equation
or T2 r3 For poles
M-1L3T-2 h<<<<<<R (h < 100 km)
There is no e
2h earth on the
use, gl= g 1-
R For equator
IMPORTANT POINTS ABOUT Note the point
THREE MASSES(EQUAL) REVOLVING The effect o
GRAVITATIONAL FORCE If h<<<<R, then decrease in the value
UNDER MUTUAL GRAVITATIONAL FORCE the value of
1. Gravitational force of g with height
V M When a body
*Always attractive in nature 2hg the poles, we
GM GM Absolute decrease = g = g - gl =
R
*Independent of the nature of medium V1 = = m (gp - g
l R 3 g g-gl 2h
between masses and presence or absence of Fractional decrease = = =
l l g g R
other bodies R
g g-gl 2h x 100
2. Are central forces, acts along the centre c Time period Percentage decrease = = x 100 =
V g g R ORBITAL V
of gravity of two bodies. M
T2 l3 Orbit at a he
3. Conservative force V
l M
Variation due to depth ‘d‛ m,V
4. Force between any two masses - h
g
Gravitational force
r
d gl = g [ 1- d
] Re
Force between earth and any other body - R g
l R
M
r
Force of gravity
M Re
FOUR EQUAL MASSES UNDER MUTUAL
GRAVITATIONAL FORCE If orbit is cl
earth‛s surfa
g dg
= g-g =
l
l GM Absolute decrease = (called minimum
V = (2 2+1) g R
VECTOR FORM 2 2l Note - for e
F21 force on 2 due to 1 g g-g l
d
y
l l 1 GM Fractional decrease = = = gR = 8 km
r12 vector from m1 to m2 V = g g R
R (2 2+1)
r12
G m1m2 2 R d
m2
-r12 l Percentage decrease = g x100
GM
m1
F21 = x100 = or = 6
r2 r122 l
T2 l3 Here R = g R R
r1 2
Very imp graph
G m1m2
x or - r12 The graphical representation of change in KE, PE OR T
r123
Similarly the value of g‛ with height and depth SATELLITE
F12 force on 1 due to 2 GRAVITY gl
GMm
Acceleration due to gravity GMe KE =
G m1m2 G m1m2 2r
