611

You visited us 611 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Law of Conservation of Mechanical Energy

A particle of...

Question

A particle of mass $m$ is fixed to one end of a light rigid rod of length $l$ and rotated in a vertical circular path about its other end. The minimum speed of the particle at its highest point must be

z e r o

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\sqrt{g l}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\sqrt{1.5 g l}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\sqrt{2 g l}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $z e r o$
Let the velocity at B be $v$ and at A be $\sqrt{4 g R}$ .
Energy conservation at A and B, $\frac{1}{2} m (\sqrt{4 g R})^{2} + 0 = \frac{1}{2} m v^{2} + m g (2 R)$
$⟹ v = 0$
Thus minimum velocity at highest point is Zero.

Suggest Corrections

Similar questions

Q. A particle of mass

m

is fixed to one end of a light rigid rod of length

l

and rotated in a vertical circular path about its other end. The minimum speed of the particle at its highest point must be:

Q. A particle of mass m is tied to a light string of length l and rotated along a vertical circular path. What should be the minimum speed at a highest point of its path so that the string does not become slack at any position?

Q. A particle is rotated in a vertical circle by connecting it to a string of length l and keeping the other end of the string fixed. The minimum speed of the particle when the string is horizontal for which the particle will complete the circle is
(a)

\sqrt{g l}

(b)

\sqrt{2 g l}

(c)

\sqrt{3 g l}

(d)

\sqrt{5 g l}

Two particles of mass 'm' each are attached to a light rod of length 'd', one at its centre and the other at a free end. The rod is fixed at the other end and is rotated in a plane at an angular speed $ω$ . Calculate the angular momentum of the particle at the end with respect to the particle at the centre.

Q. A particle is moving in a circular path in the vertical plane. It is attached at one end of a string of length

l

whose other end is fixed. The velocity at lowest point is

u

. The tension in the string is

\to T

and acceleration of the particle is

\to a

at any position. Then

\to T . \to a

is zero at highest point if

Join BYJU'S Learning Program

A particle of mass m is fixed to one end of a light rigid rod of length l and rotated in a vertical circular path about its other end. The minimum speed of the particle at its highest point must be

The correct option is A zeroLet the velocity at B be v and at A be √4gR.Energy conservation at A and B, 12m(√4gR)2+0=12mv2+mg(2R)⟹v=0Thus minimum velocity at highest point is Zero.

A particle of mass $m$ is fixed to one end of a light rigid rod of length $l$ and rotated in a vertical circular path about its other end. The minimum speed of the particle at its highest point must be

The correct option is A $z e r o$
Let the velocity at B be $v$ and at A be $\sqrt{4 g R}$ .
Energy conservation at A and B, $\frac{1}{2} m (\sqrt{4 g R})^{2} + 0 = \frac{1}{2} m v^{2} + m g (2 R)$
$⟹ v = 0$
Thus minimum velocity at highest point is Zero.