Choose any one of the following four responses :

(1) If both assertion and reason are true and the reason is the correct explanation of the assertion.

(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.

(3) If assertion is true but reason is false.

(4) If the assertion and reason both are false

Assertion : L/R and CR both have same dimensions.

Reason : L/R and CR both have dimension of time.

Concept Questions :-

Dimensions
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Difficulty Level:

Choose any one of the following four responses :

(1) If both assertion and reason are true and the reason is the correct explanation of the assertion.

(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.

(3) If assertion is true but reason is false.

(4) If the assertion and reason both are false.

Assertion : The quantity $\left(1\text{​}/\text{​}\sqrt{{\mu }_{0}{\epsilon }_{0}}\right)$ is dimensionally equal to velocity and numerically equal to velocity of light.

Reason : ${\mu }_{0}$ is permeability of free space and ${\epsilon }_{0}$ is the permittivity of free space.

Concept Questions :-

Dimensions
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Difficulty Level:

The surface tension of a liquid is 70 dyne/cm. In MKS system its value is

(1) 70 N/m

(2) 7 × 10–2 N/m

(3) 7 × 103 N/m

(4) 7 × 102 N/m

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Difficulty Level:

The SI unit of universal gas constant (R) is

(1) Watt K–1 mol–1

(2) Newton K–1 mol–1

(3) Joule K–1 mol–1

(4) Erg K–1 mol–1

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The unit of permittivity of free space ${\epsilon }_{0}$ is

(1) Coulomb/Newton-metre

(2) Newton-metre2/Coulomb2

(3) Coulomb2/(Newton-metre)2

(4) Coulomb2/Newton-metre2

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Difficulty Level:

The temperature of a body on Kelvin scale is found to be X K. When it is measured by a Fahrenheit thermometer, it is found to be X0F. Then X is

(1) 301.25

(2) 574.25

(3) 313

(4) 40

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Difficulty Level:

What are the units of $K=1\text{​}/\text{​}4\pi {\epsilon }_{0}$

(1) C2N–1m–2

(2) Nm2C–2

(3) Nm2C2

(4) Unitless

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Difficulty Level:

The SI unit of surface tension is

(1) Dyne/cm

(2) Newton/cm

(3) Newton/metre

(4) Newton-metre

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Difficulty Level:

E, m, l and G denote energy, mass, angular momentum and gravitational constant respectively, then the dimension of $\frac{E{l}^{2}}{{m}^{5}{G}^{2}}$ are

(1) Angle

(2) Length

(3) Mass

(4) Time

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Difficulty Level:

From the equation $\mathrm{tan}\theta =\frac{rg}{{v}^{2}}$, one can obtain the angle of banking θ for a cyclist taking a curve (the symbols have their usual meanings). Then say, it is

(1) Both dimensionally and numerically correct

(2) Neither numerically nor dimensionally correct

(3) Dimensionally correct only

(4) Numerically correct only