A force F is given by F = at + bt², where t is time. What are the dimensions of a and b:

(1) $ML{T}^{-3}$ and $M{L}^2{T}^{-4}$

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

(3) $ML{T}^{-1}$ and $ML{T}^0$

(4) $ML{T}^{-4}$ and $ML{T}^1$

The dimensions of the interatomic force constant are:

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

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

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

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

If the speed of light (c), acceleration due to gravity (g) and pressure (p) are taken as the fundamental quantities, then the dimension of gravitational constant is 

(1) $c^2{g}^0{p}^{-2}$

(2) $c^0{g}^2{p}^{-1}$

(3) $c{g}^3{p}^{-2}$

(4) $c^{-1}{g}^0{p}^{-1}$

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