Physics

Problem

A learner suggests that the magnitude

F

of the centripetal force acting on a body of mass

m

moving with speed

v

in a circle of radius

r

can be written in the general form

F = (2\pi)^{d} m^{a} v^{b} r^{c}

, where

a

b

c

and

d

are real numbers. (i) Using dimensional arguments, determine the values of

a

b

and

c

. (ii) Show that the numerical constant

(2\pi)^{d}

must be dimensionless, and hence comment on the possible value(s) of

d

. (iii) Write the final dimensionally correct expression for

F

. a. (i) Determine

a

b

c

using dimensional analysis. b. (ii) Show

(2\pi)^{d}

is dimensionless and comment on

d

. c. (iii) Write the final expression for

F