A particle (m=1kg) slides down in frictionless-track AOC starting from rest at a point A(height 2m). After reaching on horizontal smooth track compresses a light spring of spring constant K= 100N/m, by distance 0.5 m before coming to rest. The height (in m) of horizontal track is.........(Take `g= 10 m//s^(2)`)

Options

A. 0.65
B. 1
C. 0.75
D. 1.75

Answer

C

Explanation

`PE_(A)= PE_(C )+ SPE_(C ) rArr mgh_(A)= mgh_(C )+ (1)/(2) kx^(2)`
`rArr h_(C )= h_(A) -(kx^(2))/(2mg) = 2m- (100 xx 1)/(2 xx 1 xx 10 xx 4)m`
`=(2-1.25)m = 0.75m`