Question

Position of a body with acceleration 'a' is given by x = Ka^mt^n, here t is time. Find dimension of m and n.

Answer 1

Answer:

you can solve this question by two methods : (1) dimension method (2) comparing with formula.

let's see comparing with formula,

you know as well, s = ut + 1/2 at²

here, s is position of particle after time t.

a is acceleration and u is initial velocity of particle.

if we assume, s =x , u = 0

then, equation will be x = 1/2 at²

now comparing both equations

we get, m = 1 and t = 2

(2) dimension method :

dimension of x = [L]

dimension of a = [LT^-2]

dimension of t =[T]

now, x = Ka^mt^n

[L] = k[LT^-2]^m [T]^n

or, [LT^0] = k[L]^m[T]^(-2m+n)

comparing both sides,

m = 1,

-2m + n = 0 => n = 2

so, answer is m = 1 and n = 2