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Let us consider an equation (1)/(2)mv^(2...

Let us consider an equation `(1)/(2)mv^(2)=mgh`
Where m is the mass of the body. V its velocity , g is the acceleration due to gravity and h is the height . Check whether this equation is dimensionally correct.

Text Solution

Verified by Experts

`(1)/(2) mv^(2)= mgh`
Dimensions of LHS `(1)/(2)`= constant
=dimensionless
`[M^(1)][L^(1)T^(-2)][L^(1)]=[M^(1)L^(2)T^(-2)]`
The dimensions of RHS,
`[M^(1)][L^(1)T^(-2)][L^(1)]=[M^(1)L^(2)T^(-2)]`
`:.` Dimensions of LHS= Dimensions of RHS the equation is dimensionally correct.
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