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JEE Main 201322 AprilOnline
Exam
JEE Main
Year
2013
Date
22 April
Mode
Online
Subject
Physics
Chapter
Units and Dimensions

JEE Main 2013 · 22 April · Online · Physics · Units and Dimensions

The dimensions of angular momentum, latent heat and capacitance...

The dimensions of angular momentum, latent heat and capacitance are, respectively.

Options

  1. AML2 T1 A2, L2 T−2,M−1 L−2 T2\mathrm{ML}^2 \mathrm{~T}^1 \mathrm{~A}^2, \mathrm{~L}^2 \mathrm{~T}^{-2}, \mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^2
  2. BML2 T−2, L2 T2,M−1 L−2 T4 A2\mathrm{ML}^2 \mathrm{~T}^{-2}, \mathrm{~L}^2 \mathrm{~T}^2, \mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^4 \mathrm{~A}^2
  3. CML2 T−1, L2 T−2,ML2TA2\mathrm{ML}^2 \mathrm{~T}^{-1}, \mathrm{~L}^2 \mathrm{~T}^{-2}, \mathrm{ML}^2 \mathrm{TA}^2
  4. DML2 T−1, L2 T−2,M−1 L−2 T4 A2\mathrm{ML}^2 \mathrm{~T}^{-1}, \mathrm{~L}^2 \mathrm{~T}^{-2}, \mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^4 \mathrm{~A}^2

Correct answer

D. ML2 T−1, L2 T−2,M−1 L−2 T4 A2\mathrm{ML}^2 \mathrm{~T}^{-1}, \mathrm{~L}^2 \mathrm{~T}^{-2}, \mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^4 \mathrm{~A}^2

Step-by-step solution

Angular momentum =m×v×=\mathrm{m} \times \mathrm{v} \times\mathrm{r} =\mathrm{ML}^2  T−1\mathrm{~T}^{-1}Latent heat L=Qm=ML2 T−2M=L2 T−2\mathrm{L}=\frac{\mathrm{Q}}{\mathrm{m}}=\frac{\mathrm{ML}^2 \mathrm{~T}^{-2}}{\mathrm{M}}=\mathrm{L}^2 \mathrm{~T}^{-2} Capacitance C= Charge  P.d. =M−1 L−2 T4 A2\mathrm{C}=\frac{\text{ Charge }}{\text{ P.d. }}=\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^4 \mathrm{~A}^2
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