Question

Using the method of dimension check whether the following equations are
dimensionally correct or not.
a. s=ut+1/2atSQUARE

Answer 1

LHS:-

displacement = [M^0 L^1 T^0]

RHS:-

velocity x time = [M^0 L^1 T^-1] x [T^1]

=> [M^0 L^1 T^0]

1/2at^2 = [M^0 L^1 T^-2] x [T^1]^2

=> [M^0 L^1 T^0]

LHS=RHS

#HENCEPROVED

Answer 2

$Writing the dimensions of either side of the given equation.</p><p>LHS=8=displacement=[M0LT0]</p><p></p><p>$

$RHS=ut=velocity×time=[M0LT−1][T]=[M0LT0]</p><p></p><p>$

$and 1 \div at ^{2} 2 \\ =(acceleration)× {time}^ 2 \\ =[M0LT−2][T]2 \\ =[M0LT0]</p><p>As LHS=RHS, \\ formula \: is \: dimensionally \: \\ correct.</p><p></p><p>$