From a circular ring of mass M and radius R an arc corresponding to...

mass per unit length of the ring is

$\lambda = \dfrac{M}{2\piR}$

$∴$ Mass of remaining ring is ${M}^{'} = \lambda \times \dfrac{3}{4} ( 2\piR )$

$∴ {M}^{'} = \dfrac{3}{4}M$

Moment of inertia of remaining part is

${I}^{'} = {M}^{'}{R}^{2} = \dfrac{3}{4}M{R}^{2} = KM{R}^{2}$

$∴ K = \dfrac{3}{4}$