Question

A stone tied to the end of a 20 cm long string is whirled in a horizontal circle. If the centripetal acceleration is 9.8m/s^2, its angular speed in rad/sec is
1. 22/7
2. 7
3. 14
4. 20

Answer 1

Here is your answer

Hope this will help you

Answer 2

The angular speed of the stone is 7 rad/s

Explanation:

It is given that,

A stone tied to the end of a 20 cm long string, radius of the circle, r = 20 cm = 0.2 m

The centripetal acceleration of the stone, $a_c=9.8\ m/s^2$

We know that the centripetal acceleration of an object is given by the following formula as :

$a_c=\dfrac{v^2}{r}$

Since, $v=r\omega$

$a_c=\omega^2 r$

$\omega$ is the angular speed of the stone

$\omega=\sqrt{\dfrac{a_c}{r}}$

$\omega=\sqrt{\dfrac{9.8}{0.2}}$

$\omega=7\ rad/s$

So, the angular speed of the stone is 7 rad/s. Hence, the correct option is (2).

Learn more :

Centripetal acceleration

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