A block of 4 kg mass starts at rest and slides a distance d down a friction less incline (angle 30o) where it runs into a spring of negligible mass. The block slides an additional 25 cm before it is brought to rest momentarily by compressing the spring. The force constant of the spring is 400 N/m. The value of d is : (take g = 10 m/s²)

37.5 cm

Work done by the gravity = Change in potential energy of the spring

\(W = \Delta U\)

\((4)(10) \sin {30^o} (d+0.25) = \frac{1}{2} (0.25)^2\)

\(\Rightarrow d = 37.5 cm\)