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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

The dimensions of LHS are
`[M] [L T^(-1)]^(2) = [M] [L^(2)T^(-2)]`
`=[M L^(2) T^(-2)]`
The dimensions of RHS are
`[M][L T^(-2)] [L] = [M][L^(2) T^(-2)]`
`=[M L^(2) T^(-2)]`
The dimensions of LHS and RHS are the same and hence the equation is dimensionally correct.
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