NEET2010PhysicsUnits and DimensionsActual
Which of the following pairs does not have same dimensions ?
Options
- Aimpulse and momentum
- Bmoment of inertia and moment of force
- Cangular momentum and Planck's constant
- Dwork and torque.
Correct answer
B. moment of inertia and moment of force
Step-by-step solution
Impulse =F t = m (v₂-v₁ ) t t=m (v₂-v₁ ) = change in momentum [Impulse ]=[ Momentum ] Angular momentum, L =m v r Planck's constant, [h]=[ energy ] [ time ] [F r time )= m (v₂-v₁ ) t r t m (v₂-v₁ ) r=( change of momentum ) r [h]=[L] . Work, W= F d : Torque, = r F [W]=[ ] Moment of inertia, I=m r^2= mass ( distance )^2 Moment of force, = r F = distance force aligned & = distance change of momentum time & [ I ] [ ] . aligned Therefore, moment of inertia and moment of force have different dimensions.