Energy due to position of a particle is given by U= (Alpha) y1/2/ y+(beta), where alpha and beta are constants,y - Physics - Units And Measurements

Question

Energy due to position of a particle is given by U= (Alpha)
y1/2/ y+(beta), where alpha and beta are constants,y is
distance what is the dimension of (alpha*beta) ?

Jyoti Pant · Accepted Answer

Given,
U=α yy+βWriting dimensions of L H
S[ML2T-2]
Since,
all the terms that are added or subtracted or equated on different
sides of the equation must have the same dimensional formula
So,
[β]=[αyy]=[ML2T-2]αy -1/2=[α L-1/2]=[ML2T-2]or α=[ML5/2T-2][αβ]=[ML5/2T-2] [ML2T-2]=[M2L7/2T-4]

Energy due to position of a particle is given by U= (Alpha) y1/2/ y+(beta), where alpha and beta are constants,y is distance.what is the dimension of (alpha*beta) ?

Energy due to position of a particle is given by U= (Alpha) y^1/2/ y+(beta), where alpha and beta are constants,y is distance.what is the dimension of (alpha*beta) ?