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In a new system of units, the fundamenta...

In a new system of units, the fundamental quantities mass, length, time are replaced by acceleration 'a', density 'rho', and frequency 'f'. The dimensional fromula for the force in this system is

A

`[rhoa^(4)f]`

B

`[rhoa^(4)f^(-6)]`

C

`[rho^(-1)a^(-4)f^(6)]`

D

`[rho^(-1)a^(-4)f^(-1)]`

Text Solution

Verified by Experts

The correct Answer is:
B
`F = ma rArr rho xx "volume" a`
`"Volume" rArr L^(3) rArr [(L)/(T^(2))]^(3) T^(6) = a^(3)f^(-6)`
`F = rhoa^(4)f^(-6)`
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