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

1. Power

2. Force

3. Momentum

4. Work

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

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. $M^{-1}{L}^{-2}{T}^{-4}{A}^{-2}$

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 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

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. $ML{T}^2$

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 dimensions of resistivity in terms of \(M\), \(L\), \(T\), and \(Q\) where \(Q\) stands for the dimensions of charge, will be:
1. \(\left[M L^3 T^{-1} Q^{-2}\right]\)
2. \(\left[M L^3 T^{-2} Q^{-1}\right]\)
3. \(\left[M L^2 T^{-1} Q^{-1}\right]\)
4. \(\left[M L T^{-1} Q^{-1}\right]\)

The dimensions of coefficient of thermal conductivity is 

1. $M{L}^2{T}^{-2}{K}^{-1}$

2. $ML{T}^{-3}{K}^{-1}$

3. $ML{T}^{-2}{K}^{-1}$

4. $ML{T}^{-3}K$