Question

time period of a pendulum depends on length(l) and acceleration due to gravity(g) .find formula of time period​

Answer 1

doing this by dimension analysis method

according to principle of homogenity

dimention on LHS = RHS

T = K L^x A^y

[T]=[L^x][A^y]      

[T]=[T]     [L]=[L]    [A]=[L¹T⁻²]

[T] = [L^x][L¹T⁻²]^y

[T]=[L^(x+1y)T^-2y]

equating both  side we get    x+1y=0     x=-y   and  -2y=1  y=-1/2   ,  x=1/2

T = k √(L/A)  Here k = a onstant we know that  2π

T=1π√(L/A)