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

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)  (T/2)  (C)  2T  (D)  (T/4)

Tardigrade Admin · Accepted Answer

The time period T is T=(2 π r/v) dots(i) When the speed of the particle is doubled, its new time period becomes T' =(2 π r/2v) =(1/2) ((2π r/v))=(T/2) (Using (i))

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

$T$

$\frac{T}{2}$

$2 T$

$\frac{T}{4}$

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

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

T

2T​

2T

4T​

The time period T is T=v2πr​…(i) When the speed of the particle is doubled, its new time period becomes T′=2v2πr​=21​(v2πr​)=2T​ (Using (i))

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

$T$

$\frac{T}{2}$

$2 T$

$\frac{T}{4}$

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