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The position of a particle at time t is ...

The position of a particle at time `t` is given by the relation `x(t) = ( v_(0) /( alpha)) ( 1 - c^(-at))`, where `v_(0)` is a constant and `alpha gt 0`. Find the dimensions of `v_(0) and alpha`.

A

`[L^(-1)T^(-1)]``,[ T^(-2)]`

B

`[L^(2)T^(-1)]``,[ T^(-1)]`

C

`[LT^(-1)]``,[ T^(-1)]`

D

`[LT^(-2)]``,[ T^(1)]`

Text Solution

Verified by Experts

The correct Answer is:
`[LT^(-1)]` `,[ T^(-1)]`
From the principle of dimensionsal homogenity ,
`[ alpha t] =` dimensionless
:. `[ alpha] = [(1)/( t)] = [ T^(-1)]`
Similarly , `[x] = ([v_(0)])/([ alpha]) = [L] [T^(-1)] = [LT^(-1)]`
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