Question

:) The ratio of angular speed of a second-hand to the hour - hand of a watches
a) 60: 1
b) 72: 1
c) 720:1
d) 3600:1​

Answer 1

$\huge\underline{\underline{\bf \orange{Question-}}}$

The ratio of angular speed of a second-hand to the hour - hand of a watches.

$\huge\underline{\underline{\bf \orange{Solution-}}}$

We know that ,

In watch's second hand it takes 1 min (60s) to complete one Angular distance i.e 2π

So ,

$\implies{\sf Angular\:Speed(\omega_1)=\dfrac{2π}{60}}$

$\implies{\sf \pink{ \omega_1 = \dfrac{π}{30}\:rad/s}}$

And ,

Hour hand to watch take 12 hours (12×3600=43200s) to complete one rotation i.e 2π

$\implies{\sf Angular\:Speed(\omega_2)=\dfrac{2π}{43200} }$

$\implies{\sf \pink{\omega_2= \dfrac{π}{21600} \:rad/s}}$

$\large{\rm Ratio \: of \: second-hand \: and \:hour-hand }$

$\implies{\sf \dfrac{\omega_1}{\omega_2}=\dfrac{π/30}{π/21600} }$

$\implies{\sf \dfrac{\omega_1}{\omega_2}=\dfrac{720}{1}}$

$\implies{\bf \red{\omega_1:\omega_2=720:1} }$

$\huge\underline{\underline{\bf \orange{Answer-}}}$

Option (c) 720 : 1

Ratio of angular speed of a second-hand to the hour - hand of a watches is ${\bf \red{720:1}}$.

Answer 2

Answer:

$\large\boxed{\sf{(c)\;720:1}}$

Explanation:

We know that,

A second hand of the clock takes 60 sec (1 min) to cover an angular distance of 2π radians (360°).

Therefore angular speed = $\frac{2\pi}{60}=\frac{\pi}{30}$ rad/sec

Now, we know that,

For an hour hand to complete 1 rotation i.e 2π radians it takes 12hrs ( 12×3600 seconds).

.°. Angular speed of an hour hand =$\frac{2\pi}{43200}=\frac{\pi}{21600}$ rad/sse

.°. The required ratio of angular speed of the second hand to the hour hand

$= \dfrac{ \frac{\pi}{30} }{ \frac{\pi}{21600} } \\ \\ = \frac{1}{30} \times \frac{21600}{1} \\ \\ = \frac{720}{1}$

Hence the correct option is (c) 720:1