Given the equation \(\left(P+\frac{a}{V^2}\right)(V-b)=\text {constant}\). The units of \(a\) will be: (where \(P\) is pressure and \(V\) is volume)
1. \(\text{dyne} \times \text{cm}^5\)
2. \(\text{dyne} \times \text{cm}^4\)
3. \(\text{dyne} / \text{cm}^3\)
4. \(\text{dyne} / \text{cm}^2\)

The units of angular momentum are

1. $kg\text{}-\text{}{m}^2\text{}/\text{}{s}^2$

2. $Joule\text{}-\text{}s$

3. $Joule\text{}/\text{}s$

4. $kg\text{}-\text{}m\text{}-\text{}{s}^2$

In C.G.S. system the magnitutde of the force is 100 dynes. In another system where the fundamental physical quantities are kilogram, metre and minute, the magnitude of the force is

1. 0.036

2. 0.36

3. 3.6

4. 36

Faraday is the unit of

1. Charge

2. emf

3. Mass

4. Energy

SI unit of permittivity is:

1. $C^2{m}^2{N}^{-1}$

2. $C^{-1}{m}^2{N}^{-2}$

3. $C^2{m}^2{N}^2$

4. $C^2{m}^{-2}{N}^{-1}$

The unit of the coefficient of viscosity in S.I. system is

1. $m/kg\text{-}s$

2. $m\text{-}s\text{}/\text{}k{g}^2$

3. $kg\text{}/\text{}m\text{-}{s}^2$

4. $kg\text{}/\text{}m\text{-}s$

If C and R represent capacitance and resistance respectively, then the dimensions of RC are

                                                                                                      [Only for droppers]

1. $M^0{L}^0{T}^2$

2. $M^0{L}^{0}T$

3. $M{L}^{-1}$

4. None of the above

The frequency of vibration f of a mass m suspended from a spring of spring constant K is given by a relation of this type $f=C{m}^x{K}^y$; where C is a dimensionless quantity. The value of x and y are 

1. $x=\frac{1}{2},y=\frac{1}{2}$

2. $x=-\frac{1}{2},y=-\frac{1}{2}$

3. $x=\frac{1}{2},y=-\frac{1}{2}$

4. $x=-\frac{1}{2},y=\frac{1}{2}$

The velocity of water waves v may depend upon their wavelength $\lambda$, the density of water $\rho$ and the acceleration due to gravity g. The method of dimensions gives the relation between these quantities as: 

1. ${\mathrm{v}}^2\propto {\mathrm{g\lambda }}^{-1}{\mathrm{\rho }}^{-1}$

2. ${\mathrm{v}}^2\propto \mathrm{g\lambda \rho }$

3. ${\mathrm{v}}^2\propto \mathrm{g\lambda }$

4. ${\mathrm{v}}^2\propto {\mathrm{g}}^{-1}{\mathrm{\lambda }}^{-3}$

The equation of a wave is given by $Y=A\sin \omega (\frac{x}{v}-k)$ where $\omega$ is the angular velocity, x is length and $v$ is the linear velocity. The dimension of k is 

1. LT

2. T

3. $T^{-1}$

4. T²