Home
Class 12
PHYSICS
The diagram show a small bead of mass m ...

The diagram show a small bead of mass `m` carrying charge `q`. The bead can freely move on the smooth fixed ring placed on a smooth horizontal plane . In the same pane a charge ` +Q` has also been fixed as shown. The potential at the point ` P` due to ` +Q` is `V` . The velocity which the bead should projected from the point `P` so that it can complete a circle should be greater than .

A

`sqrt((6qV)/(m))`

B

`4sqrt((qV)/(m))`

C

`sqrt((3qV)/(m))`

D

`sqrt((7qV)/(2m))`

Text Solution

Verified by Experts

The correct Answer is:
A
If we send the bead diametrically opposite, it will complete full circle as resultant of repulsive force between the charges and normal reaction between the ring and bead will provide force in tangential direction of ring.
Hence at point `2,v_(2)=0`.
Given `(1)/(4piepsilon_(0))(Q)/(4a)=V`
or `(1)/(4piepsilon_(0))(Q)/(a)=4V`
Let velocity given at `1` be `v_(1)`, then
`(1)/(2)mv_(1)^(2)+(1)/(4piepsilon_(0))(Qq)/(4a)=0+(1)/(4piepsilon_(0))(Qq)/(a)`
or `(1)/(2)m_(1)^(2)=3Vq+qV=q-4V`
or `(1)/(2)m_(1)^(2)=3Vq` or `V_(1)=sqrt((6Vq)/m)`
Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS VOLUME 3

    CENGAGE PHYSICS ENGLISH|Exercise Assertion and Reason Type|8 Videos

  • MISCELLANEOUS VOLUME 3

    CENGAGE PHYSICS ENGLISH|Exercise Comprehension Type|94 Videos

  • MAGNETIC FIELD AND MAGNETIC FORCES

    CENGAGE PHYSICS ENGLISH|Exercise Multiple Correct Answer type|2 Videos

  • MISCELLANEOUS VOLUME 5

    CENGAGE PHYSICS ENGLISH|Exercise Integer|12 Videos

Similar Questions

Explore conceptually related problems

A short dipole of dipole moment P is placed near a point charge Q as shown in figure. Find force on the dipole due to the point charge

A short dipole of dipole moment P is placed near a point charge Q as shown in figure. Find force on the dipole due to the point charge

For the system shown in the figure, a small block of mass m and smooth irregular shaped block of mass M , both free to move are placed on a smooth horizontal plane. The minimum velocity v imparted to block so that it will overcome the highest point of M is

A very long straight wire carries a current I. At the instant when a charge +Q at point P has velocity vecV , as shown, the force on the charge is-

A point charge + q is fixed at same height as centre of an uncharged sphere placed on a smooth horizontal surface as shown in figure. Neglect the induced charges on horizontal surface. Then conducting sphere is released from rest. Then the conducting sphere

A particle of charge q is projected from point P with velocity v as shown. Choose the correct statement from the following.

Figure represents a square carrying charges +q,+q,-q,-q at its four corners as shown. Then the potential will be zero at points

A very long straight wire carries a current I. At the instant when a charge +Q at point P has velocity vecV , as shown, the force on the charge is

a very long straight wire carries a current I. at the instant when are charge -Q at point P has velocity v as shown in figure the force on the charge is

The minimum velocity v with which charge q should be projected so that it manages to reach the centre of the ring starting from the position shown in figure is