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. $M^0{L}^0{T}^0$

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

The position of a particle at time t is given by the relation $l =\frac{v_o}{\alpha }(1-e^{\alpha t})$ , where v₀ is a constant and α > 0. The dimensions of v₀ and α are respectively

1. $M^0{L}^1{T}^{-1}$ and T^–1

2. $M^0{L}^1{T}^0$ and T^–1

3. $M^0{L}^1{T}^{-1}$ and LT^–2

4. $M^0{L}^1{T}^{-1}$ and T

If radius of the sphere is (5.3 ± 0.1)cm. Then percentage error in its volume will be 

1. $3+6.01\times \frac{100}{5.3}$

2. $\frac{1}{3}\times 0.01\times \frac{100}{5.3}$

3. $\left(\frac{{\displaystyle 3\times 0.1}}{{\displaystyle 5.3}}\right)\times 100$

4. $\frac{0.1}{5.3}\times 100$