Match the graph of a pendulum of mass \"m\", speed \"v\" and length \"r\" with t

Question

Match the graph of a pendulum of mass "m", speed "v" and length "r" with the proper linearization process AND what the slope of the linearized graph means (match correct graph letter to the correct number):   

1.) square the independent variable

2.) no linearization needed

3.) take the inverse of the independent variable

4.) The linearized plot yields mass/radius

5.) the linearized plot yields speed ^2 / radius

6.) The linearized plot yields mass*speed^2

Explanation / Answer

graph a:
it is a plot between centripetal force and speed.

as we know that if speed is v and mass is M and radius of rotation is r,

then centripetal force=m*v^2/r

so if mass m and radius r are fixed, then centripetal force will be square of the speed.
hence option 1 is correct.

graph b:

as it is a plot between centripetal force and mass,

the linearized plot will yield v^2/r i.e. speed^2/radius

hence option 5 is correct.

graph c:

as it is a plot between centripetal force and raidus,

we need to take the inverse of independent variable.

option 3 is correct.

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