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  4. A particle moves with a uniform speed v and time period T in a circular path of radius r . If the speed of the particle is doubled, its new time period is

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Q. A particle moves with a uniform speed $ v $ and time period $ T $ in a circular path of radius $ r $ . If the speed of the particle is doubled, its new time period is

J & K CETJ & K CET 2016Motion in a Plane

Solution:

The time period $T$ is
$T=\frac{2 \pi \,r}{v} \dots(i)$
When the speed of the particle is doubled, its new time period becomes
$T' =\frac{2 \pi \,r}{2v} =\frac{1}{2} \left(\frac{2\pi r}{v}\right)=\frac{T}{2}$ (Using (i))