Engineering Mechanics - Moments of Inertia - Discussion

Discussion :: Moments of Inertia - General Questions (Q.No.1)

1. 

Determine the radius of gyration ky of the parabolic area.

[A]. ky = 76.5 mm
[B]. ky = 17.89 mm
[C]. ky = 78.6 mm
[D]. ky = 28.3 mm

Answer: Option B

Explanation:

No answer description available for this question.

Prabhu said: (Jul 5, 2011)  
I want explanation.

Phani said: (Aug 13, 2011)  
Can any one explain this?

Chandu said: (Aug 17, 2011)  
Hai frnds i solve it........


Ky=root over Iy/A
Iy=moment of inertia with respect to y-axis
A=area

dI=dA*r^2 (r is radius)

dI=0.1(1600-x^2)x^2 dx
integrate both sides,limits are 0 to 40
and multiple with 2

we get
I=2730666
here dA=y dx(here y=0.1(1600-x^2))
integrate both sides, limits are 0 to 40
and multiple with 2

A=8533

substitute the values of I,A in Ky we get

Ky=17.89mm

Crazy Man said: (Aug 3, 2012)  
Ky=root over Iy/A
Iy=moment of inertia with respect to y-axis
A=area

dI=dA*r^2 (r is radius)

dI=0.1(1600-x^2)x^2 dx
Integrate both sides, limits are 0 to 40
And multiple with 2

we get
I=2730666
Here dA=y dx(here y=0.1(1600-x^2))
Integrate both sides, limits are 0 to 40
And multiple with 2

A=8533

Substitute the values of I, A in Ky we get

Ky=17.89mm

Malik said: (Jun 8, 2014)  
How that I came?

Kwesiga Henry said: (May 25, 2015)  
How is the area of the figure got?

Jaduo said: (Sep 18, 2015)  
I can't understand please help me!

Sai Deep said: (Oct 26, 2015)  
Please give me explanation?

Pradeep said: (Mar 1, 2016)  
Area of parabola 4ah/3.

Kumar Saim said: (May 5, 2016)  
You are correct @Chandu.

I'm also tried in the same way, it gives the same answer as yours.

Akbar Shah said: (Nov 9, 2016)  
Can anyone provide the simple explanation?

Abdu said: (Jan 27, 2017)  
The area of semi-parabola that written in the form of x=k(y^2) or vertical semi-parabola area formula is given by 2*ab/3 so the total area will be 2*(2*ab/3) so 160*80/3= 8533 unit^2
we can take a piece of area dxdy then multiply by x^2 then integrate finally apply gyration formula.

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