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. $T$
• B. $\frac{T}{2}$
• C. $2T$
• D. $\frac{T}{4}$

Answer 1

Answer: (B)

$\frac{T}{2}$

Answer 2

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))