A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fictitious force F which is inversely proportional to R3. Its time period of revolution will be given by :
Solution
$F \propto {1 \over {{R^3}}}$<br><br>$F = {K \over {{R^3}}}$<br><br>${{m{v^2}} \over R} = {K \over {{R^3}}}$<br><br>$m{(\omega R)^2} = {K \over {{R^2}}}$<br><br>$m{\omega ^2}{R^2} = {K \over {{R^2}}}$<br><br>${\omega ^2} = {K \over m}\left( {{1 \over {{R^4}}}} \right)$<br><br>${\left( {{{2\pi } \over T}} \right)^2} \propto {1 \over {{R^4}}}$<br><br>${{4{\pi ^2}} \over {{T^2}}} \propto {1 \over {{R^4}}}$<br><br>$T \propto {R^2}$
About this question
Subject: Physics · Chapter: Rotational Motion · Topic: Conservation of Angular Momentum
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