Question 5 - A-Level Maths

Show that the moment of inertia of the object about \(L\) is \(\left( \frac { 408 + 7 \lambda } { 12 } \right) M a ^ { 2 }\).
The period of small oscillations of the object about \(L\) is \(5 \pi \sqrt { } \left( \frac { 2 a } { g } \right)\).
Find the value of \(\lambda\).