V is the volume of a liquid flowing per ...

V is the volume of a liquid flowing per second through a capillary tube of length l and radius r, under a pressure difference (p). If the velocity (v), mass (M) and time (T) are taken as the fundamental quantities, then the dimensional formula for `eta` in the relation `V=(pipr^(4))/(8etal)`

`[M V^(-1)]`

`[M^(1)V^(-1)T^(-2)]`

`[M^(1)V^(1)T^(-2)]`

`[M^(1)V^(-1)T^(-1)]`

Text Solution

Verified by Experts

The correct Answer is:

`V=(pipr^(4))/(8etal) therefore eta=(pipr^(4))/(8Vl)`
`pi` and 8 have no dimensions. Writing the dimensional formulae for all quantities, we get
`[eta]=([M^(1)L^(-1)T^(-2)][L^(4)])/([L^(3)T^(-1)][L^(1)])[because V="Volume/sec"]`
`[eta]=[M^(1)L^(-1)T^(-1)]`
But velocity `v=(L)/(T) therefore L=vT`
`therefore [eta]=[M^(1)V^(-1)T^(-1)T^(-1)]=[M^(1)V^(-1)T^(-2)]`

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If the energy (E), velocity (v) and force (F) are taken as fundamental quantities, then what is the dimensional formula for mass?

`E^(1)v^(2)F^(1)`

`F^(1)v^(-1)E^(1)`

`E^(1)v^(-2)F^(0)`

`F^(1)v^(-2)E^(0)`

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

`PV^2T^2`

`P^-1V^2T^-2`

`PVT^2`

`P^-1VT^2`

If energy E , velocity v and time T are taken as fundamental quanties, the dimensional formula for surface tension is

`[Ev^(-2) T^(-2)]`

`[E^(2) vT^(-2)]`

`[Ev^(-2) T^(-1)]`

`[E^(-2) v^(-2) T^(-1)]`