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

Let us consider an equaiton
`(1)/(2)mv^2 = mgh,`
Where m is the mass of the body, `upsilon` its velocity, g is acceleration due to gravity and h is the height. Cheak 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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