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Five particles each of mass ' m ' are kept at five vertices of

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Five particles each of mass ' $m$ ' are kept at five vertices of a regular pentagon. A sixth particle of mass ' $M$ ' is kept at centre of the pentagon ' $O$ '. Distance between ' $M$ ' and ' $m$ ' is ' $α$ '. Find
(a) net force on ' $M$ '
(b) magnitude of net force on ' $M$ ' if any one particle is removed from one of the vertices.

Name: Video solution 1: Five particles each of mass ' m ' are kept at five vertices of a regular pentagon. A sixth particle of mass ' M ' is kept at centre of the pentagon ' O '. Distance between ' M ' and ' m ' is ' α '. Find(a) net force on ' M '(b) magnitude of net force on ' M ' if any one particle is removed from one of the vertices.
Uploaded: 2022-12-06T13:13:38.000Z
Duration: 3 min
Description: Video solution 1: Five particles each of mass ' m ' are kept at five vertices of a regular pentagon. A sixth particle of mass ' M ' is kept at centre of the pentagon ' O '. Distance between ' M ' and ' m ' is ' α '. Find(a) net force on ' M '(b) magnitude of net force on ' M ' if any one particle is removed from one of the vertices.

Views: 6,892 students

Updated on: Dec 6, 2022

Book:

Mechanics Volume 2 (DC Pandey)

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Daniel Discussed

Five particles each of mass '

m

' are kept at five vertices of a regular pentagon. A sixth particle of mass '

M

' is kept at centre of the pentagon '

O

'. Distance between '

M

' and '

m

' is '

α

'. Find
(a) net force on '

M

'
(b) magnitude of net force on '

M

' if any one particle is removed from one of the vertices.

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

(a)

F_{A} = F_{B} = F_{C} = F_{D} = F_{E} = \frac{GM m}{a ^{2}} = F (s a y)

Angle between two successive force vectors is

θ = \frac{36 0 ^{\circ}}{5} = 7 2^{\circ}

.
When these five force vectors are added as per polygon law of vector addition we get another closed regular polygon as shown below.
Therefore, net resultant force on '

M

' is zero.
This result is true

(F_{net} = 0)

for any number of particles, provided masses at vertices are equal and polygon is regular.
(b) When particle at

A

is removed, then

F_{A}

will be removed. So, magnitude of net force will be

F

as shown below:
Solution Image

∴

F_{net} = F = \frac{GM m}{a ^{2}}

(b) When particle at A is removed, then

F_{A}

will be removed. So, magnitude of net force will be
F as shown below:
Solution Image

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Question Text	Five particles each of mass ' $m$ ' are kept at five vertices of a regular pentagon. A sixth particle of mass ' $M$ ' is kept at centre of the pentagon ' $O$ '. Distance between ' $M$ ' and ' $m$ ' is ' $α$ '. Find (a) net force on ' $M$ ' (b) magnitude of net force on ' $M$ ' if any one particle is removed from one of the vertices.
Updated On	Dec 6, 2022
Topic	Gravitation
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 1
Upvotes	135
Avg. Video Duration	3 min

Text solutionVerified

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