Search any question & find its solution
Question:
Answered & Verified by Expert
In which of the following pairs, the two physical quantities have different dimensions?
Options:
Solution:
2027 Upvotes
Verified Answer
The correct answer is:
Moment of inertia and moment of a force
(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
$=\left[\mathrm{M}\left[\mathrm{LT}^{-1}\right]=\left[\mathrm{MLT}^{-1}\right)\right.$
(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 $=\left[\mathrm{ML}^{2} \mathrm{T}^{-2} \mathrm{l}\right.$ and torque $=\left[\mathrm{ML}^{2} \mathrm{T}^{-2} 1\right.$
So, (c) option has different dimensions.
$=\left[\mathrm{ML}^{2} \mathrm{T}^{-1}\right]$
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
$=\left[\mathrm{M}\left[\mathrm{LT}^{-1}\right]=\left[\mathrm{MLT}^{-1}\right)\right.$
(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 $=\left[\mathrm{ML}^{2} \mathrm{T}^{-2} \mathrm{l}\right.$ and torque $=\left[\mathrm{ML}^{2} \mathrm{T}^{-2} 1\right.$
So, (c) option has different dimensions.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.