Question

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

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

Answer 1

The correct option is C

${\pi }^{2}m{s}^{-2}$ and direction along the radius towards the centre

$a=\frac{v^2}{r}={\omega }^{2}r=4{\pi }^2{n}^{2}r=4{\pi }^2{\left(\frac{22}{44}\right)}^2\times 1={\pi }^{2}m/s^2$
and its direction is always along the radius and towards the centre.