Question

An equilateral triangle is made of a string of lenth 60cm and mass 100gm. Find the moment of inertia of the triangle about perpendicular axis through centroid.​

Answer 1

Answer:

ANSWER

The centre of mass of equilateral triangle is the centroid of the equilateral triangle.

As shown in figure, OP=

2

L

tan(30

o

)=

2

3

L

Moment of inertia(MOI) of rod about centre of mass, I

cm

=

12

1

mL

2

Using parallel axis theorem of MOI, I=I

cm

+mx

2

, Where I

cm

is MOI about centre of mass and x is distance between centre of mass and axis of rotation.

MOI of the system =3(

12

1

mL

2

+m(

2

3

L

)

2

)=3×

6

1

mL

2

=

2

mL

2

solution

Explanation:

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