If $x=at+b{t}^2$, where x is the distance travelled by the body in kilometres while t is the time in seconds, then the units of b are

(1) $km\text{}/\text{}s$

(2) $km\text{}-\text{}s$

(3) $km\text{}/\text{}{s}^2$

(4) $km\text{}-\text{}{s}^2$

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. \(\text{dyne} / \text{cm}^2\)

Which is not a unit of electric field

(1) $N{C}^{-1}$

(2) $V{m}^{-1}$

(3) $J{C}^{-1}$

(4) $J{C}^{-1}{m}^{-1}$

Faraday is the unit of

(1) Charge

(2) emf

(3) Mass

(4) Energy

Unit of surface tension is

(1) $N{m}^{-1}$

(2) $N{m}^{-2}$

(3) $N^2{m}^{-1}$

(4) $N{m}^{-3}$

Dimensions of one or more pairs are same. Identify the pairs

(1) Torque and work

(2) Angular momentum and work

(3) Energy and Young's modulus

(4) Year and wavelength

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 quantities A and B are related by the relation, m = A/B, where m is the linear density and A is the force. The dimensions of B are of

1. Pressure

2. Work

3. Latent heat

4. None of the above

An athletic coach told his team that muscle times speed equals power. What dimensions does he view for muscle?

(1) $ML{T}^{-2}$

(2) $M{L}^2{T}^{-2}$

(3) MLT²

(4) L

Dimensions of strain are:

(1) $ML{T}^{-1}$

(2) $M{L}^2{T}^{-1}$

(3) $ML{T}^{-2}$

(4) $M^0{L}^0{T}^0$