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The energy E of a particle varies with t...

The energy E of a particle varies with time t according to the equation `E=E_0sin(alphat).e^((-alphat)/(betax))`, where x is displacement from mean position `E_0` is energy at infinite position and `alpha` and `beta` are constants .
Dimensional formula of `alpha` is

A

`[M^0 L^0 T^(-1)]`

B

`[M^(-1) L^0 T^0]`

C

`[M^0 L^(-1) T^0]`

D

`[M^0 L^0 T^0]`

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Knowledge Check

  • The energy E of a particle varies with time t according to the equation E=E_0sin(alphat).e^((-alphat)/(betax)) , where x is displacement from mean position E_0 is energy at infinite position and alpha and beta are constants . Dimensions of beta are

    A
    `[M^(-1) L^0 T^0]`
    B
    `[M^0 L^(-1) T^0]`
    C
    `[M^0 L^0 T^(-1)]`
    D
    `[M^0 L^0 T^0]`

  • The energy E of a particle varies with time t according to the equation E=E_0sin(alphat).e^((-alphat)/(betax)) , where x is displacement from mean position E_0 is energy at infinite position and alpha and beta are constants . Dimensions of sin((alphat)/(betax)) are

    A
    `[M^(1) L^0 T^0]`
    B
    `[M^0 L^(1) T^0]`
    C
    `[M^0 L^0 T^0]`
    D
    Invalid expression

  • The displacement of the particle varies with time according to the relation x=(k)/(b)[1-e^(-ht)] . Then the velocity of the particle is

    A
    `k(e^(-bt))`
    B
    `(k)/(b^(2)e^(-bt)0`
    C
    `kbe^(-bt)`
    D
    None of these

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