Minimum Velocity Required to move in a circle!

Classical Mechanics Level 4

A small bead of mass $m$ can move on a smooth circular wire (radius $R$ ) under the action of a force $F =\frac{Km}{r^2}$ only directed (denote constant $r$ as the position of bead from $P$ and $K$ ) towards a point $P$ with in the circle at a distance $\frac{R}{2}$ from the center.

What should be the minimum velocity of bead at the point of the wire nearest the center of force $(P)$ so that bead will complete the circle?

None of these

\sqrt{\frac{8K}{3R}}

\sqrt{\frac{3K}{2R}}

\sqrt{\frac{6K}{R}}

\sqrt{\frac{3K}{R}}

2 solutions

Sandaparthi Venkata Trinadha Murty
Mar 19, 2018

The answer is wrong upon conservation of angular momentum at point from where force acts you get the answer

Angular momentum won't conserve due to torque by normal reaction..

Sridhar Reddy - 2 years, 8 months ago

Seong Ro
Jun 2, 2015

Plz post a solution, i just got lucky

Clearly angle OKP =30 degrees Now find out the component of the force F along KO....equate this force with centripetal force...don't forget to find out "r" in terms of "R" and substitute it

Greg Elliot - 5 years, 10 months ago

Do correct me if I were wrong.

$F \cos 30^o=m \frac{v^2}{R}$ and $r=\frac{\sqrt{3}}{2}R$

Tanishq Varshney - 5 years, 5 months ago

But this doesn't gives the answer.

Tanishq Varshney - 5 years, 5 months ago

simply get the difference b/w minimum and maximum potential energy (since it follows inverse square law u are much aware abt that) and equate it to minimum ke req.

aryan goyat - 4 years, 7 months ago

Actually, the velocity is never just a value. That is the speed .

So, theoretically, the answer is None of these .

See this problem for disambiguation.

Filip Rázek - 3 years, 6 months ago

Minimum Velocity Required to move in a circle!

2 solutions

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