If the time period (T) of vibration of a liquid drop depends on surface tension (S), radius (r) of the drop and density $\left(\rho \right)$ of the liquid, then the expression of T is 

(1) $T=k\sqrt{\rho r^3/S}$

(2) $T=k\sqrt{{\rho }^{1/2}{r}^3/S}$

(3) $T=k\sqrt{\rho r^3/S^{1/2}}$

(4) None of these

The fundamental physical quantities that have same dimensions in the dimensional formulae of torque and angular momentum are 

(1) Mass, time

(2) Time, length

(3) Mass, length

(4) Time, mole

If pressure P, velocity V and time T are taken as fundamental physical quantities, the dimensional formula of force is  

(1) $P{V}^2{T}^2$

(2) $P^{-1}{V}^2{T}^{-2}$

(3) $PV{T}^2$

(4) $P^{-1}V{T}^2$

The physical quantity which has dimensional formula as that of $\frac{\text{Energy}}{\text{Mass}\times \text{Length}}$is 

(1) Force

(2) Power

(3) Pressure

(4) Acceleration

If energy (E), velocity (v) and force (F) be taken as fundamental quantity, then what are the dimensions of mass 

(1) $E{v}^2$

(2) $E{v}^{-2}$

(3) $F{v}^{-1}$

(4) $F{v}^{-2}$

A physical quantity x depends on quantities y and z as follows: x = Ay + BtanCz, where A, B and C are constants. Which of the following do not have the same dimensions? 

(1) x and B

(2) C and z^–1

(3) y and B/A

(4) x and A

Which of the following pair does not have similar dimensions  

(1) Stress and pressure

(2) Angle and strain

(3) Tension and surface tension

(4) Planck's constant and angular momentum

Out of the following which pair of quantities do not have the same dimensions?

(1) Planck's constant and angular momentum

(2) Work and energy

(3) Pressure and Young's modulus

(4) Torque & moment of inertia

Identify the pair which has different dimensions:

(1) Planck's constant and angular momentum

(2) Impulse and linear momentum

(3) Angular momentum and frequency

(4) Pressure and Young's modulus