Question

Verify equation v=u+at in dimensional analysis

Answer 1

$\huge{\underline{\underline{........Answer.........}}}$

$\large{\underline{\underline{To verify:}}}}$

$\huge\red{ v= \:u+at}$

Dimensional formula of v is [M^0LT^-1]

Dimensional formula of u is [M^0LT^-1]

Dimensional formula of a is [M^0LT-2]

Dimensional formula of t is [M^0L^0T]

L. H. S is the dimensional formula of v=[M^0LT-1]

R. H. S is the dimensional formula of u+dimensional formula of a × dimensional formula of t.

=[M^0LT-1]+[M^0LT^-2]×[M^0L^0T]

=[M^0LT^-1]+[M^0LT^-1]

=2[M^0LT^-1]

Since 2 is a dimensionless constant, therefore L. H. S = R.H.S

Hence the given equation is dimensionally correct.