The dimensions of Farad are , where Q represents electric charge [This question includes concepts from 12th syllabus]

1. $M^{-1}{L}^{-2}{T}^2{Q}^2$

2. $M^{-1}{L}^{-2}TQ$

3. $M^{-1}{L}^{-2}{T}^{-2}Q$

4. $M^{-1}{L}^{-2}T{Q}^2$

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

Dimensional formula of capacitance is 

1. $M^{-1}{L}^{-2}{T}^4{A}^2$

2. $M{L}^2{T}^4{A}^{-2}$

3. $ML{T}^{-4}{A}^2$

4. $M^{-1}{L}^{-2}{T}^{-4}{A}^{-2}$

Dimensional formula of heat energy is  

1. $M{L}^2{T}^{-2}$

2. $ML{T}^{-1}$

3. $M^0{L}^0{T}^{-2}$

4. None of these

If C and L denote capacitance and inductance respectively, then the dimensions of LC are 

1. $M^0{L}^0{T}^0$

2. $M^0{L}^0{T}^2$

3. $M^2{L}^0{T}^2$

4. $ML{T}^2$

Which of the following quantities has the same dimensions as that of energy?

1. Power

2. Force

3. Momentum

4. Work

The dimensions of "time constant" $\frac{L}{R}$ during growth and decay of current in all inductive circuit is same as that of  

1. Constant

2. Resistance

3. Current

4. Time

The period of a body under SHM is presented by $\mathrm{T}={\mathrm{P}}^{\mathrm{a}}{\mathrm{D}}^{\mathrm{b}}{\mathrm{S}}^{\mathrm{c}}$; where P is pressure, D is density and S is surface tension. The value of a, b and c are:

1. $-\frac{3}{2},\frac{1}{2},1$

2. $-1,-2,3$

3. $\frac{1}{2},-\frac{3}{2},-\frac{1}{2}$

4. $1, 2, \frac{1}{3}$

Which of the following pairs of physical quantities has the same dimensions 

1. Work and power

2. Momentum and energy

3. Force and power

4. Work and energy

The velocity of a freely falling body changes according to $g^p{h}^q$ where g is acceleration due to gravity and h is the height. The values of p and q are:

1. $1, \frac{1}{2}$

2. $\frac{1}{2}, \frac{{\displaystyle 1}}{2}$

3. $\frac{1}{2}, 1$

4. 1, 1