Q.
Four balls each of radius 10 cm and mass 1 kg, 2kg, 3 kg and 4 kg are attached to the periphery of massless plate of radius 1 m. What is moment of inertia of the system about the centre of plate?
A) 12.04 kg-$m^{2}$
B) 10.04 kg-$m^{2}$
C) 11.50 kg-$m^{2}$
D) 5.04 kg-$m^{2}$
Explanation
(b) Moment of inertia of the system about the centre of plane is given by
$I = \left\lbrack \frac{2}{5} \times 1 \times (0.1)^{2} + 1 \times (1)^{2} \right\rbrack + \left\lbrack \frac{2}{5} \times 2 \times (0.1)^{2} + 2 \times (1)^{2} \right\rbrack$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ + \left\lbrack \frac{2}{5} \times 3 \times (0.1)^{2} + 3 \times (1)^{2} \right\rbrack + \left\lbrack \frac{2}{5} \times 4 \times (0.1)^{2} + 4 \times (1)^{2} \right\rbrack$
$= 1.004 + 2.008 + 3.012 + 4.016$
$= 10.04\ kg - m^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.