Home
Class 12
PHYSICS
Three uniform spheres each having a mass...

Three uniform spheres each having a mass M and radius a are kept in such a way that each touches the other two. Find the magnitude of the gravitational force on any of the spheres due to the other two.

A

(a)`(GM^2)/(4r^2)`

B

(b)`(2GM^2)/r^2`

C

(c)`(2GM^2)/(4r^2)`

D

(d)`(sqrt3GM^2)/(4r^2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`vecF=vecF_1+vecF_2`
As `|vecF_1|=|vecF_2|`
`therefore |vecF|=2F_1 cos 30^@`
`=2(GM^2)/((2r)^3)sqrt3/2=sqrt3/4(GM^2)/r^2`
Promotional Banner

Topper's Solved these Questions

  • GRAVITATION

    VMC MODULES ENGLISH|Exercise Level-2|30 Videos

  • GRAVITATION

    VMC MODULES ENGLISH|Exercise JEE Main (Archive)|43 Videos

  • GRAVITATION

    VMC MODULES ENGLISH|Exercise LEVEL -0 Long Answer Type|3 Videos

  • GASEOUS STATE & THERMODYNAMICS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE )|111 Videos

  • INTRODUCTION TO VECTORS & FORCES

    VMC MODULES ENGLISH|Exercise JEE Advanced ( ARCHIVE LEVEL-2)|12 Videos

Similar Questions

Explore conceptually related problems

A uniform ring of mas m and radius a is placed directly above a uniform sphere of mass M and of equal radius. The centre of the ring is at a distance sqrt3 a from the centre of the sphere. Find the gravitational force exerted by the sphere on the ring.

A uniform ring of mas m and radius a is placed directly above a uniform sphere of mass M and of equal radius. The center of the ring is at a distance sqrt3 a from the center of the sphere. Find the gravitational force exerted by the sphere on the ring.

A uniform ring of mas m and radius a is placed directly above a uniform sphere of mass M and of equal radius. The centre of the ring is at a distance sqrt3 a from the centre of the sphere. Find the gravitational force exerted by the sphere on the ring.

Three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these three circles (shaded region).

In Figure 6, three circles each of radius 3-5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these three circles (shaded region).

Three rings, each of mass m and radius r , are so placed that they touch each other. Find the moment of inertia about the axis as shown in Fig.

Two vectors having equal magnitudes A make an angle theta with each other. Find the magnitude and direction of the resultant.

A solid sphere of mass m and radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in the figure. A particle of mass m' is placed on the line joining the two centres at a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if rltxlt2r

A solid sphere of mass m and radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in the figure. A particle of mass m' is placed on the line joining the two centres at a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if xgt2R

a solid sphere of mass m and radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in figure. A particle of mass m is placed on the line joining the two centers as a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if a). rltxlt2r, b). 2rltxlt2R and c). xgt2R .

VMC MODULES ENGLISH-GRAVITATION-Level-1 MCQs
  1. Let F1 be the magnitude of the gravitational force exerted on the Su...

    Text Solution

    |

  2. The distance between the centres of the Moon and the earth is D. The m...

    Text Solution

    |

  3. Three uniform spheres each having a mass M and radius a are kept in su...

    Text Solution

    |

  4. Two balls, each of radius R, equal mass and density are placed in cont...

    Text Solution

    |

  5. A solid sphere of radius R//2 is cut out of a solid sphere of radius R...

    Text Solution

    |

  6. A spherical shell has inner radius R1, outer radius R2, and mass M, di...

    Text Solution

    |

  7. The mass of a hypothetical planet is 1/100 that of Earth and its radiu...

    Text Solution

    |

  8. An astronaut on the Moon simultaneously drops a feather and a hammer. ...

    Text Solution

    |

  9. The approximate value of g (in m//s^2) at an altitude above Earth equa...

    Text Solution

    |

  10. The height at which the acceleration due to gravity becomes (g)/(9) (w...

    Text Solution

    |

  11. Weight fo a body of a mass m decreases by 1% when it is raised to heig...

    Text Solution

    |

  12. A body weight 500 N on the surface of the earth. How much would it wei...

    Text Solution

    |

  13. If a man at the equator would weigh (3//5)th of his weight, the angula...

    Text Solution

    |

  14. If the earth stops rotating, the value of ‘ g ’ at the equator will

    Text Solution

    |

  15. Neglecting air resistance, a 1.0-kg projectile has an escape velocity ...

    Text Solution

    |

  16. The escape velocity at the surface of Earth is approximately 8 km/s. W...

    Text Solution

    |

  17. An object is dropped from an altitude of one Earth radius above Earth’...

    Text Solution

    |

  18. If M be the mass of the earth, R its radius (assumed spherical) and G ...

    Text Solution

    |

  19. Each of the four corners of a square with edge a is occupied by a poin...

    Text Solution

    |

  20. Two particles, each of mass m, are a distance d apart. To bring a thir...

    Text Solution

    |