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Mass \( M \) is distributed over the rod of length \( L \). If linear mass density \( (\lambda) \) of the rod is linearly increasing with length as \( \lambda=K x \), where \( x \) is measured from one end as \& \( K \) is contact. The moment of inertia of the rod about the end perpendicular to rod where inear mass density is zero.
(1) \( \frac{K L^{2}}{3} \)
(2) \( \frac{K L^{2}}{12} \)
(3) \( \frac{2}{3} K L^{2} \)
(4) \( \frac{K L^{4}}{4} \)
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