Which of the following is different from the others in terms of units?

  • A
    Phase difference
  • B
    Mechanical equivalent
  • C
    Loudness of sound
  • D
    Poisson's ratio

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If $R$,$X_L$,and $X_C$ represent resistance,inductive reactance,and capacitive reactance respectively,then which of the following is dimensionless?

If we use permittivity $\varepsilon$,resistance $R$,gravitational constant $G$,and voltage $V$ as fundamental physical quantities,then:

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The diameter of a wire measured by a screw gauge of least count $0.001 \text{ cm}$ is $0.08 \text{ cm}$. The length measured by a scale of least count $0.1 \text{ cm}$ is $150 \text{ cm}$. When a weight of $100 \text{ N}$ is applied to the wire, the extension in length is $0.5 \text{ cm}$, measured by a micrometer of least count $0.001 \text{ cm}$. The error in the measured Young's modulus is $\alpha \times 10^9 \text{ N/m}^2$. The value of $\alpha$ is . . . . . . . (Ignore the contribution of the load to Young's modulus error calculation)

Some physical constants are given in List-$I$ and their dimensional formulae are given in List-$II$. Match the following:
List-$I$List-$II$
$(1)$ Planck's constant$(i)$ $[ML^{-1} T^{-2}]$
$(2)$ Gravitational constant(ii) $[ML^{-1} T^{-1}]$
$(3)$ Bulk modulus(iii) $[ML^2 T^{-1}]$
$(4)$ Coefficient of viscosity(iv) $[M^{-1} L^3 T^{-2}]$

The correct answer is:

The fundamental unit which has the same power in the dimensional formula of surface tension and viscosity is

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