A learner suggests that the magnitude of the centripetal force acting on a body of…

PHYSICS · Multi-part · A Level · Physics · Measurements and their errors · Measurements and their errors

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) Determine

a

b

c

using dimensional analysis. (ii) Show

(2\pi)^{d}

is dimensionless and comment on

d

. (iii) Write the final expression for

F