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AIIMS 2010
Exam
AIIMS
Year
2010
Subject
Physics
Chapter
Units and Dimensions

AIIMS 2010 · Physics · Units and Dimensions

Which of the following pairs does not have same dimensions ?

Which of the following pairs does not have same dimensions ?

Options

  1. Aimpulse and momentum
  2. Bmoment of inertia and moment of force
  3. Cangular momentum and Planck's constant
  4. Dwork and torque.

Correct answer

B. moment of inertia and moment of force

Step-by-step solution

Impulse =F×t=F \times t =m(v2−v1)t×t=m(v2−v1)=\frac{m\left(v_2-v_1\right)}{t} \times t=m\left(v_2-v_1\right) = change in momentum ∴\therefore \quad [Impulse ]=[]=[ Momentum ]] Angular momentum, L=mvr\mathrm{L}=m v r Planck's constant, [h]=[[h]=[ energy ]×[] \times[ time ]] ⇒[F×r× time )=m(v2−v1)t×r×t\Rightarrow[F \times r \times \text{ time })=\frac{m\left(v_2-v_1\right)}{t} \times r \times t ⇒m(v2−v1)×r=(\Rightarrow m\left(v_2-v_1\right) \times r=( change of momentum )×r) \times r ∴[h]=[L]\therefore \quad[h]=[L]. Work, W=F⃗⋅d⃗:W=\vec{F} \cdot \vec{d}: Torque, τ=r⃗×F⃗\tau=\vec{r} \times \vec{F} ∴[W]=[τ]\therefore \quad[W]=[\tau] Moment of inertia, I=mr2=mass⁡×( distance )2I=m r^2=\operatorname{mass} \times(\text{ distance })^2 Moment of force, τ=r⃗×F⃗=\tau=\vec{r} \times \vec{F}= distance ×\times force \begin{aligned} & \quad=\text{ distance } \times \frac{\text{ change of momentum }}{\text{ time }} \\ & \therefore \quad[\mathrm{I}] \neq[\tau] . \end{aligned} Therefore, moment of inertia and moment of force have different dimensions.
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