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 \(\tan \theta=\dfrac{rg}{v^2}\), 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 \(\text{cm/sec}\)) of a particle is given in terms of time \(t\) (in \(\text{sec}\)) by the relation \(v=at+\dfrac{b}{t+c};\) the dimensions of \(a,~b\) and \(c\) are:

1. \(a = L^{2} , \textrm{ } b = T , \textrm{ } c = L T^{2}\)

2. \(a = L T^{2} , \textrm{ } b = L T , \textrm{ } c = L\)

3. \(a = L T^{- 2} , b = L , \textrm{ } c = T\)

4. \(a = L , \textrm{ } b = L T , \textrm{ } c = T^{2}\)

From the dimensional consideration, which of the following equation is correct ?

1. $T=2\pi \sqrt{\frac{R^3}{GM}}$

2. $T=2\pi \sqrt{\frac{GM}{R^3}}$

3. $T=2\pi \sqrt{\frac{GM}{R^2}}$

4. $T=2\pi \sqrt{\frac{R^2}{GM}}$