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. $a=L,b=LT,c=T^2$

The SI unit of surface tension is

1. Dyne/cm

2. Newton/cm

3. Newton/metre

4. Newton-metre

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 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

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

1. C²N^–1m^–2

2. Nm²C^–2

3. Nm²C²

4. Unitless

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 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

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