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. $1,<mspace\; width="1em"></mspace>2,<mspace\; width="1em"></mspace>\frac{1}{3}$

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. $1,<mspace\; width="1em"></mspace>\frac{1}{2}$

2. $\frac{1}{2},<mspace\; width="1em"></mspace>\frac{{\displaystyle 1}}{2}$

3. $\frac{1}{2},<mspace\; width="1em"></mspace>1$

4. 1, 1

Which one of the following does not have the same dimensions

1. Work and energy

2. Angle and strain

3. Relative density and refractive index

4. Planck constant and energy

Which one has the dimensions different from the remaining three

1. Power

2. Work

3. Torque

4. Energy

A small steel ball of radius r is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $\eta$. After some time the velocity of the ball attains a constant value known as terminal velocity $v_T$. The terminal velocity depends on (i) the mass of the ball m, (ii) $\eta$, (iii) r and (iv) acceleration due to gravity g. Which of the following relations is dimensionally correct?

1. $v_T\propto \frac{mg}{\eta r}$

2. $v_T\propto \frac{\eta r}{mg}$

3. $v_T\propto \eta rmg$

4. $v_T\propto \frac{mgr}{\eta }$