explain moment of inertia of hollow  cone

4 years ago


Answers : (3)


Dear Amrit pal


consider this hollow cone ,now cut a ring of thickness dx at a distance x from the origin ,

   so radius of the ring will be  r'=xtanΘ         where Θ is the half angel of cone

so moment of inertia of this ring is  dI =dm r'2

   dm =[ M/πrL ]2πr'dL  where L is slant hight


so dI =[2M/rL]r'3dx/cosΘ

        =tan3Θ/cosΘ [2M/rL]x3dx

        =tan3Θ [2M/rh]x3dx

I =oh tan3Θ [2M/rh]x3dx


Please feel free to post as many doubts on our discussion forum as you can.
If you find any question Difficult to understand - post it here and we will get you
the answer and detailed  solution very  quickly.

 We are all IITians and here to help you in your IIT JEE preparation.

All the best.
Askiitians Experts

4 years ago

The problem can also be solved like this:- AS we are calculating the moment of inertia along the vertical axis, i guess we can actually bring down all the circular rings forming the cone to the base level so that we get a circular disk and the moment of inertia of a circular disk is (MR^2)/2. I want to know if i am right...

I also want to know the moment of inertia of the cone along one of its base diameters. How do i do it??(i got the answer as (3MR^3)/4L.... i am not too sure about it)

Thank You!


3 years ago

 how to find monent of inertia of solide cone?

2 years ago

Post Your Answer

More Questions On Mechanics

Ask Experts

Have any Question? Ask Experts
Post Question
Answer ‘n’ Earn
Attractive Gift
To Win!!!
Click Here for details
please explain
Since area under (a-t) graph gives change in velocity, so speed will be maximum at the instant t 4.
Manabendra Nath Gaine 3 months ago
t 4 sec.
Manabendra Nath Gaine 3 months ago
t 1 sec
Ishita Das 3 months ago
A cylindrical vessel open at the top is 20 cm high and 10 cm in diameter. A circular hole of crosssectional area 1 cm 2 is cut at the centre of the bottom of the vessel. Water flows from a...
p { margin-bottom: 0.25cm; line-height: 120%; } At steady state the flow through the hole = incoming flow. ie., Av = 10 4 cm 3 /s = 10 -2 m 3 /s A = 1 x 10 -4 m 2 , and v = Substituting the...
Mallikarjun Maram one month ago
Dear Student, You probably have the older version of the book. I have a new copy and verified in it. Incoming flow is correctly printed as 10 2 cm 3 /s, as I mentioned. Hope this helps.
Mallikarjun Maram 29 days ago
Dear Student, please check the data provided in the problem. To get the answer 5 cm, you need to have incoming flow to be 10 2 cm 3 /sec not 10 4 cm 3 /sec.
Mallikarjun Maram one month ago
can a body have a constant velocity but variable speed?
yes it can . because even if a body has uniform speed on a circular motion then too its velocity changes. thus it is not imprtant that change in speed is necessary for change in velocity ....
Saloni gordhan Rakholiya 4 months ago
PRAJVAL98 4 months ago
when we take a magnet near a tv or computer screen. There is a effect on the screen. We look orange light on it. How can it possible. Does magnet also attract electricity?
This only works on old fashioned tv screens or computer monitors, so to understand why this happens we need to know how they work. Inside a television there is a big glass chamber which has...
Nirmal Singh. 9 months ago
some times if we put a magnet near a tv for oo long, u can make bits of it magnetic and so it will always distort the colours,thish is how the colours stey there.
lokesh palingi 9 months ago
A 3.6 m long vertical pipe resonates with a source of frequency 212.5 Hz when water level is at certain height in the pipe. Find the height of water level (from the bottom of the pipe) at...
Hello Student, Please find the answer to your question Speed of sound, v = 340 m/s Let ℓ 0 be the length of air column corresponding to the fundamental frequency. Then v/4 ℓ 0 = 212.5 or ℓ 0...
Aditi Chauhan 6 months ago
Sir, I read from one book that protons flow from higher to lower potential..Then in the case of a capacitor when we connect two plates to the battery source, then the plate connected to the...
Charge on proton is equal to the charge on electron and also equal to atomic no, when this quantity put in an electric field, it flows from higher potential to lower potental. the Capacitor,...
Saurabh Kumar 2 months ago
View all Questions »