Question

A stone tied to the end of a string !m long is whirled in a horizintal cirlcle with constant speed. If the stone makes 10 revolutuons in 20seconds. what is the magnitude and direction of acceleration?

Answer 1

HELLO THERE!

Let's analyze the given data:

Radius (r) = 1 m (There's a technical fault in your question, because it seems that the SHIFT button of your keyboard has accidentally been pressed while pressing '1').

In 20 seconds, the stone makes 10 revolutions.

So, in 1 second, it makes:

$\frac{10}{20} = \frac{1}{2} revolutions$

Let ω be the angular velocity of the stone.

If n is the number of revolutions per second, then:

[tex] \omega = 2\pi n \\\\\implies \omega = \frac{2\times22\times1}{2\times7} \\\\\implies \omega = 3.142 =\pi  rad s^{-1} [/tex]

Now, we know that acceleration (centripetal acceleration) = rω²

So,

[tex] a = 1\times (\pi)^{2} ms^{-2} = \pi^{2} ms^{-2} [/tex]

Direction of this acceleration is towards the centre of the circular path.

HOPE THIS ANSWER IS SATISFACTORY...

Thanks!