Home
Class 11
PHYSICS
A positive charge Q is uniformly distrib...

A positive charge Q is uniformly distributed throughout the volume of a dielectric sphere of radius R. A point mass having charge +q and mass m is fired toward the center of the sphere with velocity v from a point at distance `r (r gt R)` from the center of the sphere. Find the minimum velocity v so that it can penetrate `(R//2)` distance of the sphere. Neglect any resistance other than electric interaction. Charge on the small mass remains constant throughout the motion.

Text Solution

Verified by Experts

The correct Answer is:
`sqrt((2KQq)/(mR)((r-R)/r+3/8))`
From the energy conservation
`(KQq)/r+1/2 mv(2)=11/8(KQq)/R+0`
`v=sqrt((2KQq)/(mR)[11/8-R/r])`
Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS

    ALLEN |Exercise Exercise-05(A)|35 Videos

  • MISCELLANEOUS

    ALLEN |Exercise Exercise-05(B)|19 Videos

  • MISCELLANEOUS

    ALLEN |Exercise Exersice-04[A]|34 Videos

  • KINEMATICS (MOTION ALONG A STRAIGHT LINE AND MOTION IN A PLANE)

    ALLEN |Exercise BEGINNER S BOX-7|8 Videos

  • PHYSICAL WORLD, UNITS AND DIMENSIONS & ERRORS IN MEASUREMENT

    ALLEN |Exercise EXERCISE-IV|7 Videos

Similar Questions

Explore conceptually related problems

A thin spherical conducting shell of radius R has a charge q. Another charge Q is placed at the centre of the shell. The electrostatic potential at a point P a distance R/2 from the centre of the shell is

A positive charge Q is uniformly distribut along a circular ring of radius R. A small tc charge q is placed at the centre of the ring per figure, Then

A bullet of mass m and charge q is fired towards a solid uniformly charge sphere of radius R and total charge +q. If it strikes the surface of sphere with speed u, find the minimum value of u so that it can penetrate through the sphere. (Neglect all resistance force or friction acting on bullet except electrostatic forces)

A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the centre of the sphere respectively are

A charge +Q is uniformly distributed over a thin ring with radius R . A negative point charge -Q and mass m starts from rest at a point far away from the centre of the ring and moves towards the centre. Find the velocity of this particle at the moment it passes through the centre of the ring .

If the potential at the center of a uniformly charged sphere of radius R is V then electric field at a distance r from the center of sphere will be ( r lt R ) : -

A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10V . The potential at the distance 3 cm from the centre of the sphere is:

A spherical cave of radius R/2 was carved out from a uniform sphere of radius R and original mass M. the center of the cave is at R/2 from the center of the large sphere. Point P is at a distance 2R from the center the large sphere and on the joing line of the two centers. the gravitational field strength g at point P is

A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre

Charge Q is distributed uniformly over a non conducting sphere of radius R. Find the electric p-0tential at distance r from the centre of the sphere r (r lt R) . The electric field at a distance r from the centre of the sphere is given as (1)/(4pi epsilon_(0)). (Q)/(R^(3))hatr . Also find the potential at the centre of the sphere .