Moment of inertia of uniform rod of mass m and length l about its one end is i. If one-fourth of its length is cut away, then moment of inertia of the remaining rod about its one end will be: options
Answers
The new moment of inertia will be 27/64 times the original moment of inertia.
Explanation:
We know that moment of inertia of a rod about it's one end is given by:
I = ML²/3
Moment of inertia of the original rod, i = ml²/3
After cutting one fourth of the rod;
new mass m' = 3m/4
new length l' = 3l/4
Hence new moment of inertia,
i' = m'l'²/3
= 3m/4 x (3l/4)² /3
= ml²/3 x 3/4 x 9/16
= i x 27/64
Hence the new moment of inertia will be 27/64 times the original moment of inertia.
Moment of the Inertia of Uniform Rod, in which axis is passing through a center is ML²/12
Now, If we want the axis to be passing from the Corner of its, then the Moment of the Inertia of it will be determined by the Parallel axis theorem.
Distance between the Center of mass and Corner is L/2.
∴ Moment of the Inertia about its corner = ML²/12 + ML²/4
= (ML² + 3ML²)/12 = ML²/3
Now, If the One fourth of the length is cut, then New length = L' = 3L/4
New mass = 3M/4
∴ New Moment of the Inertia along its side axis = 3M/4 × (3L/4)²/3
= 3/4M × 9L²/48
= 9/64 ML²
Hope it helps.