A long thin uniform rod of length L and initial mass M₀ ejects gas at opposite ends with constant exhaust velocity v_ex relative to the rod, in opposite directions prependicular to the rod.

Assuming that mass distribution remains uniform along the rod as the mass decrease due to gas loss.

i) Find the angular velocity as a function of the residual mass M of the rod. (I = ML² / 12)

ii) What is the limiting value of when M ---> 0 ?

Please draw the figure and answer the question with explanation