Question

Derive एक्सप्रेशन फॉर एस्केप वेलोसिटी​

Answer 1

Explanation:

ANSWER

A particle escapes from earth only it overcomes the gravitational

binding energy due to earth, and has zero energy in infinity

an Gravitational Binding energy =

R

−GMm

It is projected with initial velocity v

esc

so it escapes.

⇒ Initial KE=

2

1

mv

esc

2

(m: mass of body)

From conservation of energy :-

−

R

GMm

+

2

1

mv

esc

2

=0 [E=0 at ∞]

⇒

R

GMm

=

2

1

mv

esc

2

⇒v

esc

=

R

2GM

also, as g=

R

2

GM

we get ⇒v

esc

=

(

R

2

2GM

.R)

=

2gR

(Reqd)