Question

Three equal masses 2m each are placed at the vertices an equilateral triangle POR
(0) What is the force acting on a mass m placed at the centroid G of the triangle?
(ii) What is the force on mass m if the mass at the vertex P is quadrupled?
Take PG = QG = RG = 1 m
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2m
(1)
The an
2m​

Answer 1

Answer:

I solved only the 1st part of the question, hope you will be able to understand.

Explanation:

since equal forces are present at 120° , they will cancel out each other and net force will be zero.

Answer 2

When three equal masses 2m each are placed at the vertices an equilateral triangle POR

(i) The force acting on a mass m placed at the centroid G of the triangle is 0

1. Let the force of attraction between central mass and mass at each vertex be denoted by F.

2. F= (G*2m*m)/(1^2)

3. By resolving the forces along

I Horizontal axis we get Fsin(60) - Fsin(60) =0

II Vertical axis, we get F- Fcos(60) - Fcos(60)=0

(ii) The force on mass m if the mass at the vertex P is quadrupled is 6(Gm^2)

1. Let the force of attraction between central mass and mass at vertex P be denoted by F'.

2. F= (G*8m*m)/(1^2).

3. By resolving the forces along

I Horizontal axis we get Fsin(60) - Fsin(60) =0

II Vertical axis, we get F'- Fcos(60) - Fcos(60)=3F =(G*6m*m)/(1^2)= 6(Gm^2).