1.

A physical quantity Q is given by `Q=Q_(0)e^(-alphat^(2))` where t is the time and `alpha` is a constant. What is the dimensional formula for `alpha`?A. `[alpha]=[L^(0)M^(0)T^(0)]`B. `[alpha]=[L^(1)M^(0)T^(-1)]`C. `[alpha]=[L^(0)M^(0)T^(-2)]`D. `[alpha]=[L^(1)M^(1)T^(-1)]`

Answer» Correct Answer - c
`Q=Q_(0)e^(-alphat^(2))`
The power of an exponential quantity is dimensionless.
`therefore [alphat^(2)]=[L^(0)M^(0)T^(0)]`
`therefore alpha=(1)/(t^(2))=[(1)/(T^(2))]=[T^(-2)]`
`therefore [alpha]=[M^(0)L^(0)T^(-2)]`


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