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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Units and Dimensions

NTA Abhyas 2020 · Physics · Units and Dimensions

If p represents radiation pressure, C represents the speed of light...

If pp represents radiation pressure, CC represents the speed of light and qq represents radiation energy striking a unit area per second, then non-zero integers a,ba, b and cc are such that paqbCcp^{a}q^{b}C^{c} is dimensionless, then

Options

  1. Aa=1,b=1,c=−1a = 1, b = 1, c = - 1
  2. Ba=1,b=−1,c=1a = 1, b = - 1, c = 1
  3. Ca=−1,b=1,c=1a = - 1, b = 1, c = 1
  4. Da=1,b=1,c=1a = 1, b = 1, c = 1

Correct answer

B. a=1,b=−1,c=1a = 1, b = - 1, c = 1

Step-by-step solution

Here, [M0L0T0]=[ML−1T−2]a[MT−3]b[LT−1]c\left[M^{0}L^{0}T^{0}\right] = {\left[M^{}L^{- 1}T^{- 2}\right]}^{a}{\left[MT^{- 3}\right]}^{b}{\left[LT^{- 1}\right]}^{c}

Or \left[M^{0}L^{0}T^{0}\right] = {[ M}^{a + b}L^{- a + c}T^{- 2a - 3b - c}]<br/><br/>Comparingpowersof]<br/><br/>Comparing powers ofM, L and T,weget<br/><br/>we get<br/><br/>a + b = 0, - a + c = 0, - 2a - 3b = 0<br/><br/>Solving<br/><br/>Solvinga = 1, b = - 1, c = 1
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