1.The potiential energy of a particle varies with distance x from a fixed origin as v=A√x/x+B where A and B are constants.Find the dimensions of AB.
2.The refractive index of a material is given by the equation ʯ=A+B/ʎsquare where A and B are constants,ʎ is wavelength.Then find the dimensional formula for B.
3.A force is given by f=at+btsquare where t is time, what are the dimensions of a and b.
1. If the expression is U=(A•√x)/(B+x), then
[B] = m =MLºTº,
A•√m/m=J.
[A]=J•m/√m=J•√m=kg•m²•m½/s² =kg•m^(5/2)/s²=ML^(5/2) T^-2
2. [A] and [n] are dimensionless,
[B] =m² =MºL²Tº.
3.
f=At+Bt²
[A]=N/s=kg•m/s²•s= kg•m/s ³= MLT^-3,
[B]=N/s²= MLT^-4.