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 $(1\text{}/\text{}\sqrt{{\mu }_0{\epsilon }_0})$ 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.

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

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

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

What are the units of $K=1\text{}/\text{}4\pi {\epsilon }_0$

(1) C²N^–1m^–2

(2) Nm²C^–2

(3) Nm²C²

(4) Unitless

The SI unit of surface tension is

(1) Dyne/cm

(2) Newton/cm

(3) Newton/metre

(4) Newton-metre

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

From the equation $\tan \theta =\frac{rg}{v^2}$, 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

A dimensionally consistent relation for the volume V of a liquid of coefficient of viscosity η flowing per second through a tube of radius r and length l and having a pressure difference p across its end, is

(1) $V=\frac{\pi p{r}^4}{8\eta l}$

(2) $V=\frac{\pi \eta l}{8p{r}^4}$

(3) $V=\frac{8p\eta l}{\pi r^4}$

(4) $V=\frac{\pi p\eta }{8l{r}^4}$

The velocity v (in cm/sec) of a particle is given in terms of time t (in sec) by the relation $v=at+\frac{b}{t+c}$; the dimensions of a, b and c are

(1) $a=L^2,b=T,c=L{T}^2$

(2) $a=L{T}^2,b=LT,c=L$

(3) $a=L{T}^{-2},b=L,c=T$

(4) $a=L,b=LT,c=T^2$