A solid cylinder of mass 3 kg is rolling on a horizontal

A solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity 4 ms^–1. It collides with a horizontal spring of force constant 200 Nm^–1. The maximum compression produced in the spring will be :

At maximum compression the solid cylinder will stop so loss in K.E. of cylinder = gain in P.E. of spring

⇒	1	mv² +	1	Iω² =	1	kx²
	2		2		2

⇒	1	mv² +	1		mR²			v		²	=	1	kx²
	2		2		2			R				2

⇒	3	mv² =	1	kx²
	4		2

⇒	3	× 4 × (4)² =	1	× 200 x²
	4		2

⇒	36	= x² ⇒ x = 0.6 m
	100