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The position x of a particle at time t i...

The position `x` of a particle at time `t` is given by :
`x=(v_(0))/(a)(1-e^(-at))` where `v_(0)` is a constant and `a>0.`
The dimensional formula of `v_(0)` and `a` is :

A

`[M^(0)LT^(-1)]` and `[T^(-1)]`

B

`[M^(0)LT^(0)]` and `[T^(-1)]`

C

`[M^(0)LT^(-1)]` and `[T^(-2)]`

D

`[M^(0)LT^(-1)]` and `[T]`

Text Solution

Verified by Experts

The correct Answer is:
A
Here exponential has no dimension.
Thus `at=M^(0)L^(0)T^(0)`
`a=(1)/(T)=T^(-1)`
Also `v_(0)/(a)=x=L^(1)`or `v_(0)=aL^(1)`
`:.v_(0)=LT^(-1)`
Hence correct choice is `(a)`.
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