Class 11th Physics Units and Measurement

Which of the following equations is dimensionally incorrect?

Where t = time, h = height, s = surface tension, q = angle, p = density, a, r = radius, g = acceleration due to gravity, v = volume, p = pressure, W = work done, $Γ$ = torque, = permittivity, $\in$ = electric field, J = current density, L = length.

Option 1 - <p>W =  <span class="mathml" contenteditable="false"> <math> <mrow> <mi>Γ</mi> <mtext> </mtext> <mtext> </mtext> <mi>θ</mi> </mrow> </math> </span></p>

Option 2 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>h</mi> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mi>s</mi> <mtext> </mtext> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mtext> </mtext> <mi>θ</mi> </mrow> <mrow> <mi>p</mi> <mi>r</mi> <mi>g</mi> </mrow> </mfrac> </mrow> </math> </span></p>

Option 3 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>v</mi> <mo>=</mo> <mfrac> <mrow> <mi>π</mi> <mi>p</mi> <msup> <mrow> <mi>a</mi> </mrow> <mrow> <mn>4</mn> </mrow> </msup> </mrow> <mrow> <mn>8</mn> <mi>η</mi> <mi>L</mi> </mrow> </mfrac> </mrow> </math> </span></p>

Option 4 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>J</mi> <mo>=</mo> <mo>∈</mo> <mfrac> <mrow> <mo>∂</mo> <mi>E</mi> </mrow> <mrow> <mo>∂</mo> <mi>t</mi> </mrow> </mfrac> </mrow> </math> </span></p>

2 Views|Posted 8 months ago

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Answered by

Raj Pandey | Contributor-Level 9

8 months ago

Correct Option - 3

Detailed Solution:

$\to [W] = [τ θ] = [M L^{2} T^{- 2}] \to c o r r e c t$

$\to [h] = [L] = [\frac{2 s c o s θ}{ρ r g}] \to c o r r e c t$

$[v] = [L^{3}] [\frac{π p a^{4}}{8 η L}] = [L^{3} T^{- 1}] \to$ Incorrect

$\to J = ε \frac{\partial E}{\partial t} \to$ correct

$[A \overset{↓}{L}^{- 2}] [A \overset{↓}{L}^{- 2}]$

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