A uniform circular ring of mass m and radius R is placed freely on a horizontal smooth surface as shown in figure. A particle of mass m is connected to the circumference of the ring with a massless string. The particle is imparted velocity v0 perpendicular to length of string as shown. If T is tension in the string just after the particle imparted velocity, then Acceleration of point P at this instant, is

Question

A uniform circular ring of mass m and radius R is placed freely on a horizontal smooth surface as shown in figure. A particle of mass m is connected to the circumference of the ring with a massless string. The particle is imparted velocity v0 perpendicular to length of string as shown. If T is tension in the string just after the particle imparted velocity, then <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-asdo2rhoqcwd.png" /> Acceleration of point P at this instant, is (A) (4 T/3 m) (B) (T/m) (C) (2 T/m) (D) (3 T/2 m)

Tardigrade Admin · Accepted Answer

Calculate acceleration of each in ground frame.

T = m a_{c}

T . R = m R^{2} α

T = m R α

a_{P} = (a_{C} + α R)

T = m a_{c} \Rightarrow a_{c} = α R

a_{p} = \frac{2 T}{m}

$\frac{4 T}{3 m}$

$\frac{T}{m}$

$\frac{2 T}{m}$

$\frac{3 T}{2 m}$

Calculate acceleration of each in ground frame.
$T = m a_{c}$

$T . R = m R^{2} α$
$T = m R α$
$a_{P} = (a_{C} + α R)$
$T = m a_{c} \Rightarrow a_{c} = α R$
$a_{p} = \frac{2 T}{m}$

3m4T​

mT​

m2T​

2m3T​

Calculate acceleration of each in ground frame. T=mac​ T.R=mR2α T=mRα aP​=(aC​+αR) T=mac​⇒ac​=αR ap​=m2T​

$\frac{4 T}{3 m}$

$\frac{T}{m}$

$\frac{2 T}{m}$

$\frac{3 T}{2 m}$

Calculate acceleration of each in ground frame.
$T = m a_{c}$

$T . R = m R^{2} α$
$T = m R α$
$a_{P} = (a_{C} + α R)$
$T = m a_{c} \Rightarrow a_{c} = α R$
$a_{p} = \frac{2 T}{m}$