Question

the escape velocity v of a body depends upon is the acceleration due to gravity a) the acceleration due to gravity. b) radius of planet establish relation between v,g,r using dimensional method.​

Answer 1

Answer:

We know that

Escape velocity v

e = R 2GM = gR

Hence, we cant write

[v]=[g] a [R] b

[L 1T −1]=[L1 T −2] a[L1]b

[L1T −1]=[La+b][T −2a]

Comparing the power, we get

a+b=1 and −2a=−1

⇒ a= 21 and b= 21

⇒ ve = gR

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