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3-2.Motion in Plane
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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${\pi ^2}\,m\,{s^{ - 2}}$ 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 tangent to the circle.
D${\pi ^2}/4\,m\,{s^{ - 2}}$ and direction along the radius towards the centre.
Solution
$\begin{array}{l}{a_r}\, = {\omega ^2}R\\
{a_r} = {\left( {2\pi 2} \right)^2}R\\
\,\,\,\,\,\, = 4{\pi ^2}{2^2}{R^2} = 4{\pi ^2}{\left( {\frac{{22}}{{44}}} \right)^2}\,\,\left( 1 \right)\left[ {\therefore v = \frac{{22}}{{44}}} \right]\\
{a_t} = \frac{{dv}}{{dt}} = 0\\
{a_{net}} = {a_r} = {\pi ^2}m{s^{ – 2}}\,and\,direction\,along\,the\\
redius\,towards\,the\,center.
\end{array}$
Standard 11
Physics
