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A spring block system is placed on a hor...

A spring block system is placed on a horizontal rough surface as shown in the figure. The block is given velocity when the spring is in natural length. The total distance travelled by the block before if finally comes to rest is `2/k` meters. Find the value of `k`

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The correct Answer is:
5
`[5]`
`(-3)/5(50)x-(1/2xx50x^(2))=0-1/2xx5(4/5sqrt(10))^(2)`
`25x^(2)+30x-16=0impliesx=2/5` meters
So at maximum compression spring force `=50(2/5)=20N` and friction force `=3/5(50)=30N`
Hence the block will not move so distance `=2/5m`
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