Physics, asked by arya9857, 7 months ago

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

Answered by meenuplathottathil85
16

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!!!!

Answered by sonuvuce
15

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

\omega_h=\frac{2\pi}{T}=\frac{2\pi}{12} radian/hour

In 1 hour, the minute hand completes the rotation of 360°

Therefore, the angular acceleration of the minute hand

\omega_m=\frac{2\pi}{T}=\frac{2\pi}{1}=2\pi radian/hour

We know that if the angular acceleration is \omega and the radius of the circular path is R then the centripetal acceleration is given by

A=R\omega^2

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

A_h=\omega_h^2l

\implies A_h=(\frac{2\pi}{12})^2l

Similarly, centripetal acceleration due to minute hand

A_m=(2\pi)^2\times 1.5l

The ratio of centripetal acceleration of minute hand and hour hand

\frac{A_m}{A_h}=(2\pi)^2\times 1.5l\div (\frac{2\pi}{12})^2l

\implies \frac{A_m}{A_h}=(2\pi)^2\times 1.5l\times \frac{12^2}{(2\pi)^2l}

\implies \frac{A_m}{A_h}=1.5\times 144

\implies A_m:A_h=216:1

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

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