At maximum compression the solid cylinder will stop. According to law of conservation of mechanical energy Loss in kinetic energy = Gain in potential energy of spring of cylinder
1
2
mv2+
1
2
Iω2=
1
2
kx2
1
2
mv2+
1
2
(
mR2
R
)(
v
R
)2=
1
2
kx2 (∵v=Rω andd for solid cylinder,I=1/2mR^2)
1
2
mv2+
1
4
mv2=
1
2
kx2
3
4
mv2=
1
2
kx2 or x2=
3
2
mv2
k
Here,m=3kg,v=4ms−1,k=200Nm−1 Substituting the given values, we get x2=