Home
Class 11
PHYSICS
Evaluate int(R)^(oo)(GMm)/x^(2)dx...

Evaluate `int_(R)^(oo)(GMm)/x^(2)dx`

Text Solution

Verified by Experts

The correct Answer is:
`(GMm)/(R )`
`overset(oo)undersetRint(GMm)/x^(2)dx (GM m )/(x^2)dx =GM m overset(00)undersetRint(GMm)/x^(2)dx x^(-2) dx = GM m [x^(-2+1)/( - 2+1)]_R^(oo) = (GM m)/(R )`
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL TOOLS

    PRADEEP|Exercise M.C.Q|5 Videos

  • MATHEMATICAL TOOLS

    PRADEEP|Exercise Fill in the blanks|5 Videos

  • MATHEMATICAL TOOLS

    PRADEEP|Exercise Fill in the blanks|5 Videos

  • LAWS OF MOTION

    PRADEEP|Exercise Assertion- Reason Type Questions|17 Videos

  • OSCILLATIONS AND WAVES

    PRADEEP|Exercise multiple choice Questions|13 Videos

Similar Questions

Explore conceptually related problems

Evaluate int_(oo)^(R) (GMm)/(x^(2))dx

int_(1)^(oo)(dx)/(x^(2))

int_(3)^(oo)(3)/(x^(2)-1)dx

int_(0)^(oo)(1)/(3+x^(2))dx

Evaluate the following integrals (i) int_(R)^(oo)(GMm)/(x^(2))dx (ii) int_(r_(1))^(r_(2))-k(q_(1)q_(2))/(x^(2))dx (iii) int_(u)^(v)Mvdv (iv) int_(0)^(oo)x^(-1//2)dx (v) int_(0)^(pi//2)sin x dx (vi) int_(0)^(pi//2)cos x dx (vii) int_(-pi//2)^(pi//2) cos x dx

Evaluate int_(0)^(oo)((3)/(x^(2)+1))dx

Evaluate: int_(0)^(oo)(1)/((x^(2)+a^(2))(x^(2)+b^(2)))dx

Evaluate int_(0)^(oo)[(3)/(x^(2)+1)]dx where [.] denotes the greatest integer function.

Evaluate :int_(0)^(oo)e^(-x)dx

int_(0)^(oo)((1)/(x^(2)+1))dx

PRADEEP-MATHEMATICAL TOOLS-PROBLEMS FOR PRACTICE
  1. If x =at^3 and y = bt^2, find (dy)/(dx).

    Text Solution

    |

  2. If x = a cos theta and y = b sin theta, find (dy)/(dx)

    Text Solution

    |

  3. If the displacement x of a particle (in metre) is related with time (i...

    Text Solution

    |

  4. A particle starts from rest and its angular displacement (in red) is g...

    Text Solution

    |

  5. A metallic disc is being heated. Its area A ("in" m^2) at any time t ...

    Text Solution

    |

  6. A particle starts from origin with uniform acceleration. Its displacem...

    Text Solution

    |

  7. if the displacement of the particle at an instant is given by y = r...

    Text Solution

    |

  8. Intergrate the following with respect to x (i) 3sqrt(x^5) (ii) sqrtx...

    Text Solution

    |

  9. Intergrate the following functions w.r.t.x and find withinj the limits...

    Text Solution

    |

  10. Evaluate the following intergrals int(-pi//2)^(+pi//2) cos x dx

    Text Solution

    |

  11. Evaluate the following intergrals (i) int(15)^(30) cos (4x - 3)dx (i...

    Text Solution

    |

  12. Evaluate w.r.t.x , (i) "in"t x log x dx (ii) ing(x^2 - cos x +(1)/(x))...

    Text Solution

    |

  13. Evaluate (i) int0^(pi//4) sin x cos x dx (ii) int0^(pi//2) (1 + cos x)...

    Text Solution

    |

  14. Evaluate int(R)^(oo)(GMm)/x^(2)dx

    Text Solution

    |

  15. Evaluate int(40)^(50)(d theta)/(theta - theta0), where theta0 = 30^@C,...

    Text Solution

    |

  16. Evaluate : (a) int(u)^(upsilon)dv = int(0)^(t)adt (b)int(0)^(s)ds=int...

    Text Solution

    |

  17. Find the (i) surface area (ii) volume of the cylinder of length 10 cm ...

    Text Solution

    |

  18. Find the (i) surface area and (ii) volume of a shpere of radius 5cm.

    Text Solution

    |

  19. Find the (i) surface area (ii) volume of the rectangular body of dimen...

    Text Solution

    |

  20. Find the volume of the cone of height 10 cm and radius of the base 3 c...

    Text Solution

    |