Let M and l be the mass and length of the rod respectively and m be the mass of the insect. Let the insect be at a distance x from O at any instant of time t.

$$\therefore$$ x = vt ....... (i)

Angular momentum of the system about O,

$$L = \left[ {{{M{l^2}} \over {12}} + m{x^2}} \right]\omega $$

$$ = \left[ {{{M{l^2}} \over {12}} + m{{(vt)}^2}} \right]\omega $$ (Using (i))

$$ = \left[ {{{M{l^2}} \over {12}} + m{v^2}{t^2}} \right]\omega $$

As, $$\left| {\overrightarrow \tau } \right| = {{dL} \over {dt}} = {d \over {dt}}\left[ {{{M{l^2}} \over {12}} + m{v^2}{t^2}} \right]\omega $$

As $$\omega$$ and v remain constant

$$\therefore$$ $$\left| {\overrightarrow \tau } \right| = 2m\omega {v^2}t$$

$$\left| {\overrightarrow \tau } \right| \propto t$$

Hence, the graph and t is a straight line passing through the (0, 0). Option (b) represents correct plot.