Home
Class 12
PHYSICS
Four point masses each of mass m are pla...

Four point masses each of mass m are placed on vertices of a regular tetrahedron. Distance between any two masses is `r`.

A

Gravitation field at centre at zero

B

Gravitation potential at centre is `(-4 Gm)/(r)`

C

Gravitation potential energy of system in `(-6 Gm^(2))/(r)`

D

Gravitation force on one of the point mass is `(sqrt(6) Gm^(2))/(r^(2))`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`E_(g) = 0` By symmetry
Potential energy of system `= (-6 Gm^(2))/(r)`
Force between two masses `F= (Gm^(2))/(r^(2)`
Angle between any two force is `60^(@)`
`vec(F)=vec(F)_(1)+vec(F)_(2)+vec(F)_(3)`
`F_("net")^(2)=F_(1)^(2)+F_(2)^(2)+F_(2)^(2)+2 vec(F)_(1).vec(F)_(2)+2 vec(F)_(2).vec(F)_(3)+2vec(F)_(3).vec(F)_(1)`
`F_("net")^(2)=3F^(2)+3F^(2)`
`F_("net")=sqrt(6)F`
Promotional Banner

Topper's Solved these Questions

  • DAILY PRACTICE PROBLEM

    RESONANCE|Exercise DPP No.40|20 Videos

  • DAILY PRACTICE PROBLEM

    RESONANCE|Exercise DPP No.41|9 Videos

  • DAILY PRACTICE PROBLEM

    RESONANCE|Exercise DPP No.38|20 Videos

  • CURRENT ELECTRICITY

    RESONANCE|Exercise High Level Problems (HIP)|21 Videos

  • ELECTRO MAGNETIC WAVES

    RESONANCE|Exercise Exercise 3|27 Videos

Similar Questions

Explore conceptually related problems

Four point masses easch of mass 'm' are placed at four vertieces A, B, C, nd D of a regular hexagon of side 'a' as shown in figure , Find gravitational potential and field strength at the centre O of the hexagon. .

Five point masses m each are kept at five vertices of a regular pentagon. Distance of centre of pentagon from any one of the verticle is 'a'. Find gravitational potential and filed strength at centre.

(n - 1) equal point masses each of mass m are placed at the vertices of a angular n-polygon. The vacent vertex has a position vector a with respect to the centre of the polygon. Find the position vector of centre of mass.

Six point masses of mass m each are at the vertices of a regular hexagon of side l . Calculate the force on any of the masses.

Assertion : Four point masses each of mass m are placed at points 1, 2, 3 and 6 of a regular hexagon of side a. Then the gravitational field at the centre of hexagon is (Gm)/(a^(2)) Reason : The field strength due to masses at 3 and 6 are cancelled out.

Four particles each of mass m are placed at the vertices of a square of side l. the potential at the centre of square is

Four masses (each of m ) are placed at the vertices of a regular pyramid (triangular base) of side 'a'. Find the work done by the system while taking them apart so that they form the pyramid of side '2a'.

Four small point charges (each of equal magnitude q) are placed at four corners of a regular tetrahedron of side a. find out potential energy of charge system

Four particles each of mass 'm' are placed at the four vertices of a square 'a' .Find net force on any one the particle.