Question 280: Units , Dimensions and Error Analysis

Question

Which of the following set have different dimensions?

Accepted Answer

Option A
Pressure
,
YoungÃ¢ÂÂs modulus
, and
Stress
All three have the same dimensional formula:
$ M L^{-1} T^{-2} $
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All same dimensions.
Option B
EMF
,
Potential difference
, and
Electric potential
All represent
potential difference
(energy per unit charge):
$ M L^{2} T^{-3} I^{-1} $
Ã¢ÂÂ
All same dimensions.
Option C
Heat
,
Work done
, and
Energy
All represent forms of energy:
$ M L^{2} T^{-2} $
Ã¢ÂÂ
All same dimensions.
Option D
Dipole moment
,
Electric flux
,
Electric field
LetÃ¢ÂÂs write the dimensional formulas:
Electric dipole moment (p)
= charge ÃÂ distance
$   [p] = Q L = I T L   $
Electric flux (ÃÂ¦)
= $ E 	imes A $
Electric field $ E $ has $ M L T^{-3} I^{-1} $, so
$   [ÃÂ¦] = M L^{3} T^{-3} I^{-1}   $
Electric field (E)
$   M L T^{-3} I^{-1}   $
Ã¢ÂÂ These three clearly have
different dimensions
.
Ã¢ÂÂ
Answer: Option D
Explanation:
Only
Dipole moment
,
Electric flux
, and
Electric field
have different dimensional formulas; all other sets have same dimensions.

Answer

Pressure, Young's modulus, Stress

Answer

EMF, Potential difference, Electric potential

Answer

Heat, Work done, Energy

Answer

Dipole moment, Electric flux, Electric field

Units , Dimensions and Error Analysis

Which of the following set have different dimensions?

Choose the correct answer: