Question:
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
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
Updated On: Jun 8, 2024
- $ T $
- $ \frac{T}{2} $
- $ 2T $
- $ \frac{T}{4} $
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The Correct Option is B
Solution and Explanation
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))
$T=\frac{2 \pi \,r}{v} \dots(i)$
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))
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Concepts Used:
Motion in a Plane
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
- v = final velocity of the particle
- u = initial velocity of the particle
- s = displacement of the particle
- a = acceleration of the particle
- t = the time interval in which the particle is in consideration