Question

On the basis of dimensional arguments, rule out the wrong relation for Kinetic Energy. (i)`(3)/(16)m upsilon^2` (ii) `(1)/(2)m upsilon^2 + ma`

Answer 1

Correct Answer - Relation (ii) is wrong
`K.E. = (1)/(2)mv^2 = M(LT^(-1))^2 = [ML^2T^(-2)]`
`Now, (1)/(16)m v^2 = M(LT^(-1))^2 = [ML^2T^(-2)]`
:. This formula is dimensionally correct for K.E.
(ii) `(1)/(2)m upsilon +ma = M(LT^(-1))^2 +MLT^(-2)`
This is not permissibal as quantities with
different dimension cannot be added.
Hence Relation(ii) is wrong.