A ring of radius r is given a velocity v 0 in forward direction angular velocity ω=3 v 0 / r in anticlockwise direction as shown and kept on a rough plane. The curve representing the variation of velocity of center of mass ( v cm ) as a function of time t is :

Question

A ring of radius r is given a velocity v 0 in forward direction angular velocity ω=3 v 0 / r in anticlockwise direction as shown and kept on a rough plane. The curve representing the variation of velocity of center of mass ( v cm ) as a function of time t is : (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/554ba0ac59e37a657cb66249eae94f0e-.png" /> Sphere will move then backward and rolling will start m v0 R-I (3 v0/r)=m vc R+I ω vc=ω R

Q. A ring of radius $r$ is given a velocity $v_{0}$ in forward direction angular velocity $ω = 3 v_{0} / r$ in anticlockwise direction as shown and kept on a rough plane. The curve representing the variation of velocity of center of mass $(v_{c m})$ as a function of time $t$ is :

Sphere will move then backward and rolling will start
$m v_{0} R - I \frac{3 v _{0}}{r} = m v_{c} R + I ω$
$v_{c} = ω R$

Q. A ring of radius r is given a velocity v0​ in forward direction angular velocity ω=3v0​/r in anticlockwise direction as shown and kept on a rough plane. The curve representing the variation of velocity of center of mass (vcm​) as a function of time t is :

Sphere will move then backward and rolling will start mv0​R−Ir3v0​​=mvc​R+Iω vc​=ωR

Q. A ring of radius $r$ is given a velocity $v_{0}$ in forward direction angular velocity $ω = 3 v_{0} / r$ in anticlockwise direction as shown and kept on a rough plane. The curve representing the variation of velocity of center of mass $(v_{c m})$ as a function of time $t$ is :

Sphere will move then backward and rolling will start
$m v_{0} R - I \frac{3 v _{0}}{r} = m v_{c} R + I ω$
$v_{c} = ω R$