First slide

Moment of intertia

Question

The figure shows a uniform rod lying along the X-axis. The locus of all the points lying on the XY-plane, about which the moment of inertia of the rod is same as that about O is

Moderate

A

an ellipse
B

a circle
C

a parabola
D

a straight line

Solution

If the axis passes through the point (x,y) , then $m [{(x - \frac{l}{2})}^{2} + y^{2}] + \frac{1}{12} m l^{2} = \frac{1}{3} m l^{2} \Rightarrow {(x - \frac{l}{2})}^{2} + y^{2} = {(\frac{l}{2})}^{2}, w h i c h r e p r e s e n t s a c i r c l e o f r a d i u s \frac{l}{2} w i t h i t s c e n t r e a t (\frac{l}{2}, 0) .$

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