A ring of radius R rolls without slipping on a rough horizontal surface with a constant velocity. The radius of curvature at the highest point of the path followed by any particle on the ring is

Question

A ring of radius R rolls without slipping on a rough horizontal surface with a constant velocity. The radius of curvature at the highest point of the path followed by any particle on the ring is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-bkwnrxwuii357mcf.jpg" /> (A) 5R (B) 2R (C) 4 R (D) none of these

Tardigrade Admin · Accepted Answer

Radius of Curvature is given by =(( textvelocity)2/ textNormal Acceleration) =((2 v)2/v2/R)=4R <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-bkwnrxwuii35vt25.jpg" />

Q. A ring of radius $R$ rolls without slipping on a rough horizontal surface with a constant velocity. The radius of curvature at the highest point of the path followed by any particle on the ring is

$5 R$

$2 R$

$4 R$

none of these

Radius of Curvature is given by
$= \frac{( velocity ) ^{2}}{Normal Acceleration}$
$= \frac{( 2 v ) ^{2}}{v ^{2} / R} = 4 R$

Q. A ring of radius R rolls without slipping on a rough horizontal surface with a constant velocity. The radius of curvature at the highest point of the path followed by any particle on the ring is

5R

2R

4R