Question

Q) An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then the dimensional formula of constant of proportionality is?

Answer 1

viscous force = k * velocity

here k is the constant having dimensions [ M^x L^y T^z] ,

and the force has the dimensions of [ M¹ L ¹ T^-2]

and velocity have the dimensions of [ M⁰ L ¹ T^-1]

the dimensions of viscous force must be equal that of (k * velocity)

which yields x+0=1 therefore x=1

y+1=1 therefore y =0

z-1=-2 therefore z= -1

and hence the dimensions of k becomes [ M¹ L⁰ T^-1]