Home
Class 11
PHYSICS
A charged particle is shot with speed V...

A charged particle is shot with speed V towards another ifxed charged particle Q .It approaches Q up to a closest distnce r and then returns.If q were given a speed 2V, the closest distance of approach would be

A

r

B

2r

C

`r//2`

D

`r//4`

Text Solution

Verified by Experts

The correct Answer is:
D
At the distance of closest approach
`K_("Initial")=PE_("final")`
`1/2 mv^(2)=(Kq_(1)q_(2))/r_(0)rArr r_(0) prop 1/v^(2)`
Hence `r_(20)/r_(10)=(v_(1)/v_(2))^(2)=(v/(2v))^(2)=1/4 rArr r_(20)=r_(10)/4`
Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS

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

  • MISCELLANEOUS

    ALLEN|Exercise MCQ s WITH ONE OR MORE THAN ONE CORRECT ANSWER|6 Videos

  • MISCELLANEOUS

    ALLEN|Exercise Exersice-04[B]|16 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|8 Videos

Similar Questions

Explore conceptually related problems

A charged particle q is shot from a large distance towards another charged particle Q which is fixed, with speed v. It approaches Q up to as closed distance r and then returns. If q were given a speed 2v, the distasnce of approach would be

A charge particle 'q' is shot towards another charged particle 'Q' which is fixed, with a speed 'v'. It approaches 'Q' upto a closest distance r and then returns. If q were given a speed of '2v' the closest distances of approach would be

A long straight wire carries a current i. A particle having a positive charge q and mass m, kept at distance x_0 from the wire is projected towards it with speed v. Find the closest distance of approach of charged particle to the wire.

Rutherford model: The approximate size of the nucleus can be calculated by using energy conservation theorem in Rutherford's alpha -scattering experiment. If an alpha -particle is projected from infinity with speed v towards the nucleus having Z protons, then the alpha -particle which is reflected back or which is deflected by 180^@ must have approached closest to the nucleus .It can be approximated that alpha particle collides with the nucleus and gets back. Now if we apply the energy conservation equation at initial point and collision point then: (P.E.)_i= 0 , since P.E. of two charge system separated by infinite distance is zero. Finally the particle stops and then starts coming back. 1/2m_alpha v_alpha^2+0=0+(Kq_1q_2)/Rimplies 1/2m_alphav_alpha^2=K(2exxZe)/R implies R=(4KZe^2)/(m_alphav_alpha^2) Thus the radius of nucleus can be calculated using above equation. The nucleus is so small a particle that we can't define a sharp boundary for it An alpha -particle with initial speed v_0 is projected from infinity and it approaches up to r_0 distance from a nuclie. Then, the initial speed of alpha -particle, which approaches upto 2r_0 distance from the nucleus is :

Two identical particles of mass m carry a charge Q , each. Initially one is at rest on a smooth horizontal plane and the other is projected along the plane directly towards first particle from a large distance with speed v. The closest distance of approach be .

A charged particle of charge 'Q' is held fixed and another charged particle of mass 'm' and charge 'q' (of the same sign) is released from a distance 'r'. The impulse of the force exerted by the external agent on the fixed charge by the time distance between 'Q' and 'q' becomes 2 r is

A charge particle q_(1) , is at position (2, -1, 3). The electrostatic force on another charged particle q_(2) at (0, 0, 0) is :

An alpha - particle moving with initial kinetic energy K towards a nucleus of atomic number z approaches a distance 'd' at which it reverse its direction. Obtain the expression for the distance of closest approach 'd' in terms of the kinetic energy of alpha - particle K.

A particle of mass m and charge +q approaches from a very large distance towards a uniformly charged ring ofradius Rand charge, mass same as that of particle, with initial velocity v_(0) along the axis of the ring as shown in the figure-1.420. What is the closest distance of approach between the ring and the particle? Assume the space to be gravity free and frictionless :

A charge particle q of mass is placed at a distance d from another charge particle -2q of mass 2 m in a uniform magnetic field B as shown if particle are projected towareds each other with equal speed v_(0) , so that the two particle touches each other without collision during its motion (Assume only force due to magnetic field acts on the particle)

ALLEN-MISCELLANEOUS-Exercise-05(A)
  1. A thibn spherical conducting shell of radius R has a charge q. Another...

    Text Solution

    |

  2. Two spherical conductors B and C having equal radii and carrying equal...

    Text Solution

    |

  3. A charged particle is shot with speed V towards another ifxed charged...

    Text Solution

    |

  4. Four charges equal to-Q are placed at the four corners of a square and...

    Text Solution

    |

  5. A charged ball B hangs from a silk thread S, which makes an angle thet...

    Text Solution

    |

  6. Two point charge +8q and -2q are located at x = 0 and x = L, respectiv...

    Text Solution

    |

  7. Two thin wire rings each having radius R are placed at distance d apar...

    Text Solution

    |

  8. An electric dipole is placed at an angle of 30° to a non-uniform elect...

    Text Solution

    |

  9. Two spherical conductors A and B of radii 1 mm and 2mm are separated b...

    Text Solution

    |

  10. An electric charge 10^(-3) muC is placed at the origin (0, 0) of xy-co...

    Text Solution

    |

  11. Charges are placed on the vertices of a square as shown in figure belo...

    Text Solution

    |

  12. The potential at a point x (measured in mu m) due to some charges situ...

    Text Solution

    |

  13. A thin conducting spherical shell of radius R has charge Q spread unif...

    Text Solution

    |

  14. A charge Q is placed at each of the opposite corners of a square. A ch...

    Text Solution

    |

  15. This question contains statements-1 and Statement-2. Of the four choic...

    Text Solution

    |

  16. Two points P and Q are maintained at the potentials of 10V and -4V res...

    Text Solution

    |

  17. Let P(r) = (Q)/(pi R^(4)) r be the charge desntiy distribution for a s...

    Text Solution

    |

  18. Charge q is uniformly distributed over a thin half ring of radius R. T...

    Text Solution

    |

  19. Let there be a spherically symmetric charge distribution with charge d...

    Text Solution

    |

  20. Two identical charged sphere are suspended by strings of equal length....

    Text Solution

    |