Question

A bead of mass m can slide freely along a smooth vertical ring of radius R. The maximum angular velocity of the ring about a vertical axis for which the lowest position of ring would be the only steady position of the bead, is given by

• A. $\sqrt { \frac { 2 g } { R } }$
• B. $\sqrt { \frac { g } { R } }$
• C. $\sqrt { \frac { g } { 2 R } }$
• D. $\sqrt { \frac { g } { 4 R } }$

Answer 1

Answer: (B)

$\sqrt { \frac { g } { R } }$

Answer 2

N cosθ = mg

N sinθ = mω²(R sinθ)

∴ cosθ = g/ω²R

For θ = 0, ω = $\sqrt { \frac { g } { R } }$

Hence the correct choice is