Moment of inertia is a physical term which oppose the change in rotational motion. Moment of inertia depends on distribution of mass, shape of the body as well as distance from the rotational axis. Moment of linear momentum is called angular momentum. If no external torque act on the system then angular momentum of the system remains conserved. Geometrical meaning of angular momentum relates to the areal velocity.
(i) Mass M is distributed over the rod of length L. If linear mass density ( λ ) linearly increases with length as λ = Kx. The M.I. of the rod about one end perpendicular to rod i.e. (YY ′ )–
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Ans.
(i)
Sol.
Fig.
= 
= 
= 
. x 3 dx = 
So choice is correct and rest are wrong.
(ii)
Sol. If M is mass of the square plate.
Mass of portion of each hole
m = 
π R 2 = 
M
Moment of Inertia of remaining portion
I = I square – 4 I hole
[16R 2 + 16R 2 ] – 4 
I = 
MR 2
(iii)
Sol. From definition of angular momentum
= 
× 
= mv × 
= 
= 
= 
mv.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems