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NEET
Exam
NEET
Subject
Physics
Chapter
Units and Dimensions

NEET · Physics · Units and Dimensions

If and S respectively denote the coefficient of viscosity and...

If η\eta and SS respectively denote the coefficient of viscosity and surface tension of a liquid, then the ratio ηS\dfrac{\eta}{S} has the dimensions of:

Options

  1. A[M0L1T−1][M^0 L^1 T^{-1}]
  2. B[M0L−1T1][M^0 L^{-1} T^1]
  3. C[M2L−1T−3][M^2 L^{-1} T^{-3}]
  4. D[M0L−2T1][M^0 L^{-2} T^1]

Correct answer

B. [M0L−1T1][M^0 L^{-1} T^1]

Step-by-step solution

Dimensional formula for the coefficient of viscosity, [η]=[ML−1T−1][\eta] = [M L^{-1} T^{-1}]

Dimensional formula for surface tension, [S]=ForceLength=[MLT−2][L]=[MT−2][S] = \dfrac{\text{Force}}{\text{Length}} = \dfrac{[M L T^{-2}]}{[L]} = [M T^{-2}]

Now, taking the ratio:
\left[\dfrac{\eta}{S}\right] = \dfrac{[M L^{-1} T^{-1}]}{[M T^{-2}]} = [M^0 L^{-1} T^1]<br><br>Answer:<br><br>Answer:[M^0 L^{-1} T^1]
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