what is the ratio of the Centripetal acceleration of the tip of the minute and hour hand of a clock. If minute hand is 1.5 times longer than the hour hand
Answers
Answer:
The answer is 216
Explanation:
Centripetal acceleration(ac)=V^2/R
V=Rw, thus ac=R^2w^2/R=Rw^2
And w=2₹/T ( please consider ₹as pie)
Now time period of minute hand =60*60=3600sec
And its length is 1.5 times more than the length of hour hand, let us take length of hour hand as r, then minute hand has length 1.5r
Then w=2₹/3600
Then ac1=1.5r(2₹/3600)^2m/s^2--------(1)
Similarly time period of hour hand =12*60*60=43200sec
Then w=2₹/43200
Thus ac2=r(2₹/43200)^2m/s^2---------(2)
(1)/(2)=ac1/ac2
1.5*r*2₹*2₹*43200*43200/r*2₹*2₹*3600*3600
=1.5*43200*43200/3600*3600
=216//
That's it!!!
Hope it was helpful!!!!
The ratio of the Centripetal acceleration of the tip of the minute and hour hand of a clock is 216:1
Explanation:
Let the length of hour hand be l
Then, length of minute hand = 1.5l
In 12 hours, the hour hand completes rotation of 360°
Therefore, the angular acceleration of the hour hand
radian/hour
In 1 hour, the minute hand completes the rotation of 360°
Therefore, the angular acceleration of the minute hand
radian/hour
We know that if the angular acceleration is and the radius of the circular path is R then the centripetal acceleration is given by
Here the length of the hour and minute hands will be equal to the radius of their circular paths
Therefore,
Centripetal acceleration due to hour hand
Similarly, centripetal acceleration due to minute hand
The ratio of centripetal acceleration of minute hand and hour hand
Hope this answer is helpful.
Know More:
Q: The ratio of the angular speeds of the hour hand and the minute hand of a clock is:
Click Here: https://brainly.in/question/41716