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Question

A stone tied to the end of a string 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolutions in 44 seconds, what is the magnitude and direction of acceleration of the stone?

A
π2 ms2 and direction along the radius towards the centre.
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B
π2 ms2 and direction along the radius away from the centre.
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C
π2 ms2 and direction along the tangent to the circle.
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D
π24 ms2 and direction along the radius towards the centre.
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Solution

The correct option is A π2 ms2 and direction along the radius towards the centre.
We know that the angular velocity ω=2πf, where f is the frequency.
It is also given that the stone makes 22 revolutions in 44 seconds.
Hence, f=2244=0.5 Hz
So, ω=2πf=π.

We also know that,
ac=ω2R=π2(1)=π2 m/s2


As it is moving with constant speed, tangential acceleration
at=dvdt=0
Therefore, net acceleration
anet=ar=π2ms2
and direction along the radius towards the centre.

Hence option A is the correct answer.

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