Question

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

• A. $\frac{\pi^2}{4}$ms-2 and direction along the radius towards the centre
• B. 2$\pi^2$ ms-2 and direction along the radius away from centre
• C. $\pi^2$ ms-2 and direction along the radius towards the centre
• D. 4$\pi^2$ ms-2 and direction along the tangent to the circle

Answer 1

Answer: (C)

$\pi^2$ ms-2 and direction along the radius towards the centre

Answer 2

Given, String length is 1 m.
In 44 seconds, a stone makes 22 rotations.
Stone thus completes $\frac{22}{44}$ revolutions in 1 second, making frequency = $\frac{22}{44}$ sec 1 = $\frac{1}{2}$ Hz.
We are aware that angular speed = 2 frequency w = 2 $\frac{1}{2}$= rad/sec.
Now, acceleration equals a=2r, where r is the radius or string length.
Acceleration = $\frac{1 }{ 9.8596}$ m/s2

Therefore, the correct option is (C): $\pi^2$ ms-2 and direction along the radius towards the centre