Answer:
A. China rose
B. Methyl red
C. Phenolphthalein
Explanation:
An indicator is a substance used to detect the presence of an acid or base as characterized by the indicators color change. An indicator can either be natural or synthetic depending on whether it is obtained from naturally occurring substance (natural) or synthesized in a laboratory (synthetic).
A. China rose is a type of natural indicator that turns deep PINK or MAGENTA in the presence of an acid or GREEN in the presence of a base.
B. Methyl red is a synthetic Indicator that turns RED in the presence of an acid or YELLOW in the presence of a base.
C. Phenolphthalein is an organic dye that is originally colorless but turns PINK in the presence of a base but remains colorless in the presence of an acid or neutral substance.
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(a) 
The relationship beween centripetal acceleration and angular speed is

where
is the angular speed
r is the radius of the circular path
Here we gave
is the centripetal acceleration
r = 5.15 m is the radius
Solving for
, we find:

(b) 21.3 m/s
The relationship between the linear speed and the angular speed is

where
v is the linear speed
is the angular speed
r is the radius of the circular path
In this problem we have

r = 5.15 m
Solving the equation for v, we find
