PhysicsUnits and Measurements

Velocity v, acceleration a and force f are taken as fundamental quant…

Velocity v, acceleration a and force f are taken as fundamental quantities, then angular momentum will have the dimension :

Answer & explanation

Correct answer: option 1

Angular momentum (L) ∝ v^x a^y f^z

ML²T^-1 = (LT^-1)^x (LT^-2)^y (MLT^-2)^z

ML²T^-1 = M^z L^x+y+z T^-x-2y-2z

1 = z

2 = x + y + z ⇒ x + y = 1

-1 = -x - 2y - 2z ⇒ x + 2y = 1 - 2 = -1

∴ y = -2

x + y = 1

⇒ x = -y = 2

∴ Angular momentum (L) = v² a ^-2 f