IIT JEE , AIEEE Forum - Physics , Mechanics

Ank999

Four particles having masses m , 2m , 3m and 4m are placed at the four corners of a square of edge a . Find the gravitational force acting on a particle of mass m placed at the centre .

r_madhu_1

Just draw a neat diagram for this question.
Use the formula
F=G(m1)(m2)/r^2 and find the force vectors for each four forces ech corresponding to one pair of centrally located mass and the corner located mass.
Show this in the diagram.
Now, Add the vector-add the forces to get the resultant force.
If you want the vector form of the force, you can assume the centrally located mass at the origin.

lokeshsardana

Answer comes out to be

4sqrt(2) Gm²/a²

Greatdreams

ya both of the above answers are correct 4 root 2Gm^2/a^2 is the correct answer

edison

Q) Four particles having masses m , 2m , 3m and 4m are placed at the four corners of a square of edge a . Find the gravitational force acting on a particle of mass m placed at the centre .

Ans)

(m)A.....................B(2m)

.

. (m)O

.

.(4m)C...................D(3m)

Force at cente due to masses at A and D = F₁

where F₁= 2G(3m-m)m/a^{2_{= 4}}Gm² / a² along OD

Similarly due to masses at C and B is = F₂

or F₂ = 4Gm² / a² along OC

Thus resultant of F₁ and F₂ which are equal perpendicular to each other = F =

{(F₁)²+ (F₂)^{2_{} =}}4(

2)Gm² / a²

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