For a bubble P pressure - density- E energy- so the dimension of P56-12 E13 is the dimension of -

Give that the time period T of ossilation of a gas bubble from an explosion under water depends uopon P, D and E ehere P is the static pressure, D is the density of water and E is the total energy of explosion, find dimensionally the relation of T.

The velocity $v$ of sound in a gas depends upon its pressure $P$ and density $ρ$ , shown by using dimensional analysis, show that $ν \propto \sqrt{\frac{P}{ρ}}$

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For a bubble P pressure ρ density, E energy, so the dimension of P56ρ12E13 is the dimension of _________.

The correct option is D velocity.For a bubblePressure=PDensity=ρEnergy=Eρ5/6P1/2E1/3=(MT−2)5/6×(ML1/2)×(MLT−2)1/3=LT−1Velocity

For a bubble $P$ pressure $ρ$ density, $E$ energy, so the dimension of $P^{\frac{5}{6}} ρ^{\frac{1}{2}} E^{\frac{1}{3}}$ is the dimension of _________.

The correct option is D velocity.
For a bubble
Pressure $= P$
Density $= ρ$
Energy $= E$
$ρ^{5 / 6} P^{1 / 2} E^{1 / 3} = (M T^{- 2})^{5 / 6} \times (M L^{1 / 2}) \times (M L T^{- 2})^{1 / 3} = L T^{- 1} V e l o c i t y$