A block of mass 8 kg is released from the top of an inclined smooth surface as shown in figure. If spring constant of spring is 200 Nm^(-1) and block comes to rest after compressing spring by 1 m then find the distance travelled by block before it comes to rest

Explanation

Consider d is the distance travelled by block along the plane and height it comes in downward direction `h=d sin 30^(@)`
Now, when block will came to rest, the decrease in its potential energy will store in spring
`therefore" "mgh=(1)/(2)ky^(2)" [y is compression in spring ]"`
`rArr" "mg d sin 30^(@)=(1)/(2)ky^(2)`
`rArr" "8xx10xx(d)/(2)=(1)/(2)xx200xxt^(2)`
`rArr" "40d=100`
`rArr" "d=2.5m`