Question

A bead of mass m is located on a parabolic wire with its axis vertical and vertex directed towards downward as in figure and whose equation is x² = ay. If the coefficient of friction is m, the highest distance above the x-axis at which the particle will be in equilibrium is –

• A. µa
• B. µ²a
• C. $\frac { 1 } { 4 } \mu ^ { 2 } a$
• D. $\frac { 1 } { 2 } \mu \mathrm { a }$

Answer 1

Answer: (C)

$\frac { 1 } { 4 } \mu ^ { 2 } a$

Answer 2

For the sliding not to occur when tan q £ µ

tanq = $\frac { d y } { d x }$ = $\frac { 2 \mathrm { x } } { \mathrm { a } }$ = $\frac { 2 \sqrt { \mathrm { ya } } } { \mathrm { a } }$ = $2 \sqrt { \frac { \mathrm { y } } { \mathrm { a } } }$

$2 \sqrt { \frac { \mathrm { y } } { \mathrm { a } } }$ £ µ or y £ $\frac { a \mu ^ { 2 } } { 4 }$