The dimensional formula of angular velocity is

(1) $M^0{L}^0{T}^{-1}$

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

(3) $M^0{L}^0{T}^1$

(4) $M{L}^0{T}^{-2}$

Dimensional formula for angular momentum is

 (a) $M{L}^2{T}^{-2}$

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

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

(4) $M^0{L}^2{T}^{-2}$

The dimensional formula for r.m.s. (root mean square) velocity is

(1) $M^{0}L{T}^{-1}$

(2) $M^0{L}^0{T}^{-2}$

(3) $M^0{L}^0{T}^{-1}$

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

The dimensional formula for Planck's constant (h) is 

(1) $M{L}^{-2}{T}^{-3}$

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

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

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

Out of the following, the only pair that does not have identical dimensions is 

(1) Angular momentum and Planck's constant

(2) Moment of inertia and moment of a force

(3) Work and torque

(4) Impulse and momentum

The dimensional formula for impulse is same as the dimensional formula for 

(1) Momentum

(2) Force

(3) Rate of change of momentum

(4) Torque

Which of the following is dimensionally correct

(1) Pressure = Energy per unit area

(2) Pressure = Energy per unit volume

(3) Pressure = Force per unit volume

(4) Pressure = Momentum per unit volume per unit time

Planck's constant has the dimensions (unit) of 

(1) Energy

(2) Linear momentum

(3) Work

(4) Angular momentum

The equation of state of some gases can be expressed as $\left(P+\frac{{\displaystyle a}}{{\displaystyle V^2}}\right)(V-b)=RT$. Here P is the pressure, V is the volume, T is the absolute temperature and a, b, R are constants. The dimensions of ‘a’ are 

(1) $M{L}^5{T}^{-2}$

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

(3) $M^0{L}^3{T}^0$

(4) $M^0{L}^6{T}^0$