Physics - Unit & Dimension Question with Solution | TestHub

(a) Planck's constant = Energy
$=\left[{\mathrm{ML}}^2{\mathrm{T}}^{-1}\right]$
Angular momentum = Moment of inertia Angular velocity
$=\left[{\mathrm{ML}}^2\right]\times \left[{\mathrm{T}}^{-1}\right)=\left[{\mathrm{ML}}^2{\mathrm{T}}^{-1}\right]$
(b) Impulse = Force x Time
$=\left[{\mathrm{MLT}}^{-2}\right]\mathrm{IT}=\left[{\mathrm{MLT}}^{-1}\right]$
and linear momentum = Mass $\times$ Velocity
$=[\mathrm{M}\left[{\mathrm{LT}}^{-1}\right]=\left[{\mathrm{MLT}}^{-1}\right)$
(c) Moment of inertia = Mass $\times (\text{ Distance }{)}^2$
$=\left[M{L}^2\right]$
and moment of force = Force x Distance
$=\left[{\mathrm{MLT}}^{-2}\right]\mathrm{U}=\left[{\mathrm{M}}^2{\mathrm{T}}^{-2}\right]$
(d) Energy $=[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\mathrm{l}$ and torque $=[{\mathrm{ML}}^2{\mathrm{T}}^{-2}1$
So, (c) option has different dimensions.