The physical quantity which has the dimensional formula ${M}^{1}{T}^{-3}$ is

(1) Surface tension

(2) Solar constant

(3) Density

(4) Compressibility

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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 $ML{T}^{1}$

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The dimensions of inter atomic force constant are

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

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

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

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

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

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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

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$M{L}^{3}{T}^{-1}{Q}^{-2}$is dimension of

(1) Resistivity

(2) Conductivity

(3) Resistance

(4) None of these

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Dimension of electric current is

(1) $\left[{M}^{0}{L}^{0}{T}^{-1}Q\right]$

(2) $\left[M{L}^{2}{T}^{-1}Q\right]$

(3) $\left[{M}^{2}L{T}^{-1}Q\right]$

(4) $\left[{M}^{2}{L}^{2}{T}^{-1}Q\right]$

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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

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

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

(1) Force

(2) Power

(3) Pressure

(4) Acceleration

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