Question

Taking "force" F, "length" L and "time" T to be the fundemental equations , find the dimensions of (a) density (b) pressure (c ) momentun and (d) energy

Answer 1

a) density we know is simply mass divided by volume

We know the dimensions of mass and volume i.e,

Mass is M and volume is L^3

Therefore, dimension of density,rho will be ML^3

B) we know that pressure,P is mothing but force upon area and we know very well the dimensions of both.

Therefore, the dimensions of pressure,P will be ML^-1T^-2

C) the formula for momentum we know is p=mv

And the dimensions of mass and velocity are known to us.

Therefore, the dimension of momentum will be nothing but

MLT^-1

D) we know energy is nothing but work done whose formula is forcex displacement and we know the dimensions of force and displacement.

The dimensions of force is MLT^-2 amd displacement is L

Therefore, dimensions of energy os nothing but

ML^2T^-2