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Question

The position of a particle at time t is given by the relation x=v0α(1eαt). The dimensional formula for α2 v30 will be :

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Solution

x=v0α(1eαt)....(A)

From equation (A) since exponential is dimensionless

αt is dimensionless quantity

αt=[M0L0T0]

[α]=[M0L0T0][T]

[α]=[M0L0T1]...(1)

Also,

[v0α]=[x]

[v0]=[x][α]...(2)

from (2) and (1)

[v0]=[x][α]=[L][M0L0T1]


=[M0L1T1]....(3)

Dimensional formula of α2 v03 can be obtained from from (1) and (3)

= [M0L0T1]2 [M0L1T1]3

=[M0L3T5]

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