Consider the adjacent figure . A knife of mass 1 kg slides on a frictionless wedge of mass 5 kg between two frictionless guides. At the instant shown, the spring has initial compression of 1 m. The ground is also frictionless. The velocity of the wedge when the knife edge is about to touch the ground `(6k)/(sqrt(89))m//s`. find the value of k. ( AsSigmae the spring to be ideal also for large compression)

Explanation

Let `V_(w)=` velocity of wedge
By conservation of mechanical energy
`1xx10 xx 3 + 1/2 xx 1 xx 1^(2)= 1/2xx1xx(3/2 V_(w))^(2)+1/2xx5(V_(w))^(2)+1/2xx1xx5^(2)`
`rArr V_(w)=(24)/(sqrt(89))`m/s
Hence `k=4`