Question

Using dimensional analysis derive the relation F = ma. Where the symbols have the usual meaning.

Answer 1

Force on a body depends on mass(m), acceleration (a) an

F α m^aa^bt^c

M¹L¹T^-2 = M^a(LT^-2)^bT^c

M¹L¹T^-2 = M^aL^bT^-2a+c

Equating the powers, we get a = 1 ,b = 1, -2b + c = -2, c = 0

F = m¹a¹t⁰ = ma.