Total Price:

There are no items in this cart.
Continue Shopping

How to find the moment of inertia of a solid cone about its central axis..??

4 years ago


Answers : (2)


2087_16302_moment of inertia of a cone about axis.jpg


Please approve !

4 years ago

Dear student,

The moment of inertia of a cone about its central axis, start with the standard Intertia equation

I = integral r^2 dm

dm = rho dV (rho is density) (dV is basically volume)

dV = r dr dtheta dx

not going to prove that here but you will see in the integral that this does indeed form the volume. integral will be refered to as int from here on.

This now forms the triple integral

I = rho int(0 to H) int(0 to 2pi) int(0 to r) r^3 dr dtheta dx

solving the integral leaves

I = rho int(0 to H) int(0-2pi) 1/4 r^4 dtheta dx

solving the second integral leaves

I = rho int(0 to H) 1/2 pi r^4 dx

ok so now you have to sub in the equation for r (the radius) of the cone

r = (R/H)x

this is the radius at the base divided by the height of the cone multiplied by the distance along the x axis. this equation gives you r at any point this gives you

I = rho int(0 to H) 1/2 pi [(R/H)x]^4 dx

time to do some housekeeping and take all the constants outside the integral

I = (rho pi R^4) / (2 H^4) int(0 to H) x^4 dx

this can now be solved and simplified to

I = (rho pi R^4 H) / 10

At this stage your solution is complete, however you can tidy up the equation by taking out the mass term.

m = (rho pi H R^2) / 3

split the Inertia term up to serperate out the mass term

I = [(rho pi H R^2) / 3]*[ (3R^2)/10 ]

this is now the complete solution in terms of mass

I = (3mR^2)/10

4 years ago

Post Your Answer

More Questions On IIT JEE Entrance Exam

Ask Experts

Have any Question? Ask Experts
Post Question
Answer ‘n’ Earn
Attractive Gift
To Win!!!
Click Here for details
hi , i am preparing for iitjee 2016. i want a good reference for maths in algebra and tell me whether i can go with cengage learning .has it got enough sums to it’s theory...
cengage is one of the good books available in the market. good option bro
Abhishek Singh 2 months ago
cengage is one of the good books available in the market. good option bro
Abhishek Singh 2 months ago
Hi I’m from bangalore. I had missed IIT with a really small margin. Now I’m in Engineering 1 st semister. I have 8 months left. How shall I plan to study? P.S: It takes a litle time to...
Coaching is a super structure providing –planned regime and expert guidance but ultimately it’s the students who have to work hard to crack the exams. 1. The students must remain...
Harishwar 5 months ago
You will face a lot problems in juggling with JEE preparation and dealing with the academic committments of your college. You need to make a trade off between the two, i.e., given somebody a...
Aziz Alam 5 months ago
Find the locus of the mid point of the chord of a circle x 2 + y 2 = 4 such that the segment intercepted by the chord on the curve x 2 - 2x – 2y =0 subtends a right angle at the origin.
ohh , really?? have you even tried to draw the figure urself ??? all the segments intercepted on this curve inside the circle subtend an obtuse angle
abhidon3 4 months ago
well its a correct question
Vikrant Prasad 4 months ago
hey man ,, why you guyz post such a question which are either wong or incompete ,, it wastes too much time ,,,
abhidon3 4 months ago
Hi, Shiv Nadar is one of the private universities amongst many other. It is very risky to go into any provate university as you dont know exactly about there placement prospects and other...
Yash Baheti 4 months ago
Hello student, Your question is not clear and seems to be incomplete. Please recheck your question andpost it again. Thanks and regards Shaik Aasif askIITians faculty
is pradeep enough for iit 15 advanced for mastering physical chemistry except mole concept bcoz i dont understand it from pradeep.and is inorganic enough from pradeep?.
You should read NCERT well for basic understanding and if you are preparing for iit-jee, as it is the first and most requirement! Then you can understand the concepts by any standard book...
Naveen Kumar 5 months ago
View all Questions »