Please wait...
Contact Us
Need assistance? Contact us on below numbers

For Study plan details

10:00 AM to 7:00 PM IST all days.

For Franchisee Enquiry



Thanks, You will receive a call shortly.
Customer Support

You are very important to us

For any content/service related issues please contact on this number

93219 24448 / 99871 78554

Mon to Sat - 10 AM to 7 PM

there is a cubic frame,on each corner a pont mass'm' are kept,tell  about momet of inertia if axis is  pass through body diagonal of cube.each side of cube is 'a'.

Asked by Kunal 5th December 2017, 4:49 PM
Answered by Expert
Let m1, m2,.....m8 are the point masses placed at each corner of the cube.  let r be the perpendicular distance from m1 to axis of rotation.
the distance r can be calculated from the triangle area shown in figure and the required equations are given below

begin mathsize 12px style capital delta space equals space square root of s left parenthesis s minus square root of 3 a right parenthesis left parenthesis s minus a right parenthesis left parenthesis s minus square root of 2 a right parenthesis end root space equals space 1 half open parentheses square root of 3 a close parentheses space r
w h e r e space s space equals fraction numerator a left parenthesis square root of 3 plus square root of 2 plus 1 right parenthesis over denominator 2 end fraction space
r space equals space fraction numerator 2 capital delta over denominator square root of 3 a end fraction space end style
as per my calculation I am getting r = (0.816)a
m2 and m8 are placed in the axis itself, hence do not contribute for moment of Inertia.
for all other 6 masses the perpendicular distance can be calculated as explained above and all the perpendicular distances are identical.
hence required Moment of Inertia = 6 × m × (0.816)2 × a2 = 3.995 ma2
Answered by Expert 6th December 2017, 3:29 PM
Rate this answer
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10

You have rated this answer /10

Your answer has been posted successfully!

Chat with us on WhatsApp