Deduce the dimensional formula for the following physical quantities : (i) Young's modulus (ii) Co-efficient of viscosity (iii) Surface tension (iv) Bulk modulus (v) Force constant.

Deduce the dimensional formula for the following physical quantities :

1.	Deduce the dimensional formula for the following physical quantities : (i) Young's modulus (ii) Co-efficient of viscosity (iii) Surface tension (iv) Bulk modulus (v) Force constant.
Answer» Solution :(i) Young.s `=("Longitudinal stress")/("Longitudinal strain")` `=(F"/"A)/(trianglel"/"l)= (F)/(A)(l)/(trianglel)` `[Y]= ([MLT^(-2)][L])/([L^(2)][L])= [ML^(-1)T^(-2)]` (ii) Coefficient of viscosity, `eta= ("Force")/("AREA"xx"Velocity gradient")` `=("Force")/("Area")xx("Distance")/("Velocity")` `[eta]=([MLT^(-2)][L])/([L^(2)][LT^(-1)])= [ML^(-1)T^(-1)]` (iii) Surface tension, `SIGMA= ("Force")/("Length")` `[sigma]=([MLT^(-2)])/([L])= [ML^(0)T^(-2)]` (iv) BULK modulus `=("Pressure applied")/("Relative decrease in volume")` `(P)/(triangleV"/"V)=(P)/(triangleV)V` `=("Force")/("Area")(V)/(triangleV)=([MLT^(-2)][l^(3)])/([L^(2)][L^(3)])` `[ML^(-1)T^(-2)]` (v) Force CONSTANT `=("Force")/("Displacement")` `=([MLT^(-2)])/([L])= [ML^(0)T^(-2)]`.