Question

To keep on object moving in a circle at constant speed requires a force F αm^av^br^c. According to dimensional analysis the a, b, c are –

• A. a = 1, b = 2, c = –1
• B. a = 1, b = 2, c = 1
• C. a = 0, b = 2, c = – 1
• D. a = 1, b = 2, c = 0

Answer 1

Answer: (A)

a = 1, b = 2, c = –1

Answer 2

F ∝ m^av^br^c

i.e. [F] = [m]^a [v]^b [r]^c

or[M¹L¹T^-2] = [M^a] [L¹T^-1]^b[L]^C

or[M¹L¹T^-2] = [M^aL^b+cT^-b]

comparing LHS and RHS

a = 1, b + c = 1 & –b = –2

⇒ a = 1, b = 2, c = –1