Question

A L shaped rod whose one rod is horizontal and other is vertical is rotating about a vertical axis as shown with angular speed w. The sleeve shown in figure has mass m and friction coefficient between rod and sleeve is m. The minimum angular speed w for which sleeve cannot sleep on rod is –

• A. $\omega = \sqrt { \frac { \mathrm { g } } { \mu \ell } }$
• B. $\omega = \sqrt { \frac { \mu \mathrm { g } } { \ell } }$
• C. $\omega = \sqrt { \frac { \ell } { \mu g } }$
• D. None of these

Answer 1

Answer: (B)

$\omega = \sqrt { \frac { \mu \mathrm { g } } { \ell } }$

Answer 2

V = u + at

v² = u² + 2as

0 = u + (– µg)t

0 = u² + 2(– µg) s

t = $\frac { \mathrm { u } } { \mu \mathrm { g } }$

u = $\sqrt { 2 \mu \mathrm { gs } }$

t = $\frac { \sqrt { 2 \mu \mathrm { gg } } } { \mu \mathrm { g } }$ ̃ t µ $\frac { 1 } { \sqrt { \mu } }$