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If velocity (V) , force (F), and energy ...

If velocity (V) , force (F), and energy (E) are taken as fundamental units , then find the dimensional formula for mass.

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To find the dimensional formula for mass when velocity (V), force (F), and energy (E) are treated as fundamental units, we can follow these steps: ### Step 1: Establish Relationships We start by expressing mass (M) in terms of velocity (V), force (F), and energy (E) as follows: \[ M = K \cdot V^A \cdot F^B \cdot E^C \] where K is a constant and A, B, C are the powers we need to determine. ### Step 2: Write the Dimensional Formulas ...
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Knowledge Check

  • Suppose speed of light (c), force (F) and kinetic energy (K) are taken as the fundamental units, then the dimensional formula for mass will be

    A
    `[Kc^(-2)]`
    B
    `[KF^(-2)]`
    C
    `[cK^(-2)]`
    D
    `[Fc^(-2)]`

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

    A
    `E^(1)v^(2)F^(1)`
    B
    `F^(1)v^(-1)E^(1)`
    C
    `E^(1)v^(-2)F^(0)`
    D
    `F^(1)v^(-2)E^(0)`

  • Let force F, length L and time T be taken as fundamental units, then what will be the dimensional formula for mass?

    A
    `[FL^(-1)T^2]`
    B
    `[FLT^(-2)]`
    C
    `[FL^(-1)T^(-1)]`
    D
    `[FL^5T^2]`

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