# Check the dimensional consistency of the following .. 1) x=x0+u0t+1/2at2. x,x0=position,u0=velocity , a= acceleration , t=time.. 2)u=(1/2l)root t/m.. L= length, u= frequency, t= force, m= mass/unit length.. 3) v= root 2gr.. V= velocity, a= acceleration due to gravitation, r= radius of the planet.

1
by Sanup5577

2014-07-29T23:21:53+05:30

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X = x0  + u0 t  +1/2 a t²
dimention of  x  = length L
dim of  x0  =  length  L
dim of  u0  = velocity = distance/time = L / T
dim of t  = time  T
dim a =  change in  velocity / time  =  L/T /T  =   L / T²
=>  L  =  L + L/T * T + L/T² * T²
=>  all terms have same dimension L and LHS and RHS have same dimension.

2)    n  =  1/2 l  √( t/m )
n has  1 / T  as it is frequency ie., 1 / time period
l  is length  L
t =  force tension =  mass * acceleration = M L / T²          (acceleration i showed above)
m = mass / unit length  =  M / L
LHS =  1 / T      R H S  =  1/ L    *  √ ( M L / T² ) / (M / L)
R HS =  1/ L  * √ (L²/T²)      =  1 / L * L / T =  1 / T

3)
v  =  √ 2 g r
L H S =  distance/time = L / T
g = acceleration  = change in velocity / time =  L / T  / T  = L / T²
R HS  =  √ L/T²  *  L      = √ L² / T²  = L / T