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 come in downward direction `h=dsin30^(@)`. Now, when block will comes to rest, the distance in its potential energy will store in spring
`:. mgh=(1)/(2)ky^(2) " "` (y is compression in spring )
`implies mg " d " sin30^(@)=(1)/(2)ky^(2)`
`implies 8xx10xx(d)/(2)=(1)/(2)xx200xx1^(2)`
`implies` 40 d=100
`implies` d=2.5 m