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3-2.Motion in Plane
medium
એક કણ $25\, cm$ ત્રિજ્યા વાળા એક વર્તુળમાં $2$ ભ્રમણ/સેકન્ડ ના દરે ગતિ કરે છે. તો કણનો $meter/second^2$ માં પ્રવેગ કેટલો થાય?
A${\pi ^2}$
B$8\,{\pi ^2}$
C$4\,{\pi ^2}$
D$2\,{\pi ^2}$
(AIIMS-2012)
Solution
$\begin{array}{l}
Here\,T = \frac{1}{2}\sec \,the\,required\,centripetal\\
acceleration\,for\,moving\,in\,a\,circle\,is\\
{a_C} = \frac{{{v^2}}}{r} = \frac{{{{\left( {r\omega } \right)}^2}}}{r} = r{\omega ^2}r \times {\left( {2\pi /T} \right)^2}\\
so\,{a_c} = 0.25 \times {\left( {2\pi /0.5} \right)^2}\\
\,\,\,\,\,\,\,\,\,\,\, = 16{\pi ^2} \times .25 = 4.0{\pi ^2}
\end{array}$
Here\,T = \frac{1}{2}\sec \,the\,required\,centripetal\\
acceleration\,for\,moving\,in\,a\,circle\,is\\
{a_C} = \frac{{{v^2}}}{r} = \frac{{{{\left( {r\omega } \right)}^2}}}{r} = r{\omega ^2}r \times {\left( {2\pi /T} \right)^2}\\
so\,{a_c} = 0.25 \times {\left( {2\pi /0.5} \right)^2}\\
\,\,\,\,\,\,\,\,\,\,\, = 16{\pi ^2} \times .25 = 4.0{\pi ^2}
\end{array}$
Standard 11
Physics
