Question

The eacape velocity of a body depend upon (i) acceleration due to gravity (g) (ii) radius of the plate (R ) Obtain the formula for escape velcoity using the mehtod of dimensions.

Answer 1

Correct Answer - `K = sqrt(gR)`
Let `upsilon = K g^a R^b, …(i)`
where K is dimensionless constant
`[M^0L^1 T^(-1)] = (LT^(-2))^a L^b = M^0 L^(a+b) T^(-2a)`
Applying the principal of homogeneity of
dimensions, we get
a+b =1 ….(ii)
`-2a =-1, a =1//2`
From (ii) `b=1 -a =1 - (1)/(2) =(1)/(2)`
Putting these values in (i), we get
`upsilon = K g^(1//2) R^(1//2) = Ksqrt(gR)`