question_answer

A stone tied to the end of a string of 1 m 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) \[{{\pi }^{2}}\text{m}{{\text{s}}^{-2}}\] and direction along the radius towards the center.

B) \[{{\pi }^{2}}\text{m}{{\text{s}}^{-2}}\] and direction along the radius away from the center.

C) \[{{\pi }^{2}}\text{m}{{\text{s}}^{-2}}\] and direction along the tangent to the circle.

D) \[{{\pi }^{2}}\text{/4m}{{\text{s}}^{-2}}\] and direction along the radius towards the center.

Correct Answer: A

Solution :

[a] \[{{\text{a}}_{\text{r}}}-{{\omega }^{\text{2}}}\text{R}\]

\[{{a}_{r}}={{\left( 2\pi 2 \right)}^{2}}R=4{{\pi }^{2}}{{2}^{2}}R\]

\[\text{=}\,\text{4}{{\pi }^{2}}{{\left( \frac{22}{44} \right)}^{2}}\left( 1 \right)\text{    }\left[ \because \text{v}=\frac{22}{44} \right]\].

\[{{\text{a}}_{\text{t}}}\text{=}\frac{\text{dv}}{\text{dt}}=0\]

\[{{a}_{net}}=\text{ }{{a}_{t}}={{\pi }^{2}}m{{s}^{-\,2}}\] and direction along the radius towards the center.