Question

the escape velocity depends on acceleration due to gravity of the planet,radius of the planet.establish the relation between them by dimensional analysis​

Answer 1

Answer:

We know that

Escape velocity v

e

=

R

2GM

=

gR

Hence, we cant write

[v]=[g]

a

[R]

b

[L

1

T

−1

]=[L

1

T

−2

]

a

[L

1

]

b

[L

1

T

−1

]=[L

a+b

][T

−2a

]

Comparing the power, we get

a+b=1 and −2a=−1

⇒ a=

2

1

and b=

2

1

⇒ v

e

=

gR