Gravitational Potential and Escape Velocity, Lecture notes of Physics

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Gravitation

→ :

Universal law

of gravitation ?'É~ (^) Gravitational face (^) of

attraction

~ b/w these two (^) masses (E)

f ✗^ MIMZ

Fam :# ✗ ¥ f- = Gm~-?÷ G→^ universal^ Gravitational^ comet

9=6.67× 15

" mmHg

Direction of gravitational^ foeee

is

always attractive → ^.

Vector four of universal law^ of (^) gravitation . Y ' am, Ñte→=→z

• is^ i=ñ_ñ ñ

§ .

M

☐ F- (^) i=μ÷=ri >

×

Hi-FI f%→ force^ due^ to^ mass^ ② on^ mats^ ① f→μ→ ✗ 71 "^ "^ ①^ " (^) In ② ñi-9:;÷_i=G;;÷-¥y=amˢˢlñ-ñ ) F-ñP

Faia ;;÷ =-¥m;÷¥,=-;÷;→ñ fi,=

• f? So gravitational faeces^ fans^ action reaction (^) pair. force due^ to^ multiple masses Supn# pup : (^) Gravitational fare of attraction b/w any

two masses^ in^

system is independent on presence of

other masses in

system

. but resultant (^) Joke on a mass is^ vector^ fun^ of all^ the^ faeces.

Éet= (^) Ñ+É=fi8G

§) ↑ = -3-

② find location where Inky mess must^ be^ placed on line joining

bar mass So that

experience

net Reece (^). 9.7-a (^) 7.2-a47 liter __

f, 2kg

Fry

R -^ Fz

oh , =

§ (5)

= 3m

G¥#

G←Yj a = ¥

(5) 22m

9-

I z=¥

0 £? Three^ messes^ ace^ placed To (^) on vertices F, of equilateral jF ① ʰf?¥FsF^

Aref side e.^.^ find neem c- a→m force on

any

one of the mass. ☒ HE/^

= Gma

=F

a- (^) fie

• (^) Ba :'-( ↑ (^) ) ① ② Of M (^) - a -

masses are (^) places on § a^ 7- (^) a

vertices

of square

.^ find 7 Fr ✓zf=F%

net

fake on^ mass^ Ma Mo ¥ ,

F. = Gma7- i Eet (^) = FT^ c-^ FT^ c-^ f)

= a

?_? / (

'ñ)↑+ (

¥r§]

• %?-(^

E) (^ i + ↑ ) Gravitation field (^) Intensity Mo É

• , L

Gravitation field Intensity

due to a^ mass at

some (^) distance is fake pee^

wit mais^

placed at that point^ . → É=Gm→- (^) E=f÷

it

IÉ/

GAME unity field (^) %

Ys

Direction of field^

is

always in (^) the (^) direction of force acting on a^ mess^ at^ Thet point .

at

/ Ek G- el

• m

> I

Eat

-^ it

zing

find

point

i

e' siren.'S 2- honk ' E- on line joining Fe

= EL

| Ig a ¥ 1 liter __^ yo.^ two^ masses where met G (^) field :÷=9÷ (^) is deco . 4=gI(407= dr=3_g( (^48215) -

Plot graph b/w^ field^ due to^ masses^ and^ distance on line joining both mass.es (^) - I (^) I ¥,^ ←^ Er ←Er 25

%

E- (^) É - É = (^0) - G÷(-imE3^ i s¥ E- Gang

m① ( " [③ find net^ field at^ A. a i^ ¥ 1 __^ =aˢ

É at

> E.

,^ =^ *?

' ÷ ) (^) too. > Ez

> F}

1%1--11%

§÷→

> Ey E. =%÷c :^) E- = 9, . ↑ = GIT in Fiera Et^ Et^ Est^ ET +^

• É mu (^) arm = (^). + (^) EI (^) + ¥
• (^) ( E. (^) +7,9=+927) ↑

E=fdE= (^) 97-2%1=47-1-1- "

L

=

• Gy / E- (^) E) = -1% E- a :-, " oil Rod^ of

lined mass

F-

• (^) l & " density 4--40×^2

'"° ,,

✗=L > (^) ✗

✗◦^ →^ Constant

find field at point

A.

dim -_^ ✗^ die^

≥ Xok2dk

= "%¥÷, 0

field due to

uniform (^) ring at (^) point on^ its^ axis. dm ↑

M→ Total^ mass

grig R ᵈÉ (^) andesite (^) R→ Radius of (^) tiny ◦ dE% 0 I %__ᵈ¥fd☒μ

Is Ñ+Ñ

DE

d

' 'm