First slide

Dimensions of physical quantities

Question

Given equation $\frac{1}{2} m v^{2} = m g h,$ where m is the mass of the body, v is velocity, g is the acceleration due to gravity and h is the height. Then the given equation is

Easy

A

dimensionally incorrect
B

dimensionally correct
C

wrong
D

None of above

Solution

Given, $\frac{1}{2} m v^{2} = m g h$
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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