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The length if an arc traversed by minute hand of a watch 1 cm long after 15 minute as?

1 Answer
Mar 8, 2018

Answer:

This should be the radius times the angular displacement in radians, written as #pi/2# cm.

Explanation:

It can be defined that Arc length = Angle(rad)*Radius. Radians are dimensionless, so we don't need to do any conversion!

We know the radius to be 1 cm, but we don't know the angle explicitly.

What we do know is that a full revolution of a minute hand means the hand rotated #2pi# radians, in 1/60 increments (1 increment for each minute in an hour)

Therefore, we can use a basic ratio to figure out the number of radians 15 minutes gives

#15/60 = x/(2pi)#

#1/4*2pi=x#

#pi/2=x#

Now that we know the angular displacement, we can calculate the arclength:

#1cm * pi/2 = pi/2 cm#