A particle move in a straight line with retardation proportional to its displacement its loss of kinectic energy for any displacement `x` is proportional to

Options

A. `x`
B. `e^(2)`
C. `x^(2)`
D. `log_(e) x`

Answer

C

Explanation

(c ) Given : retardation prop distacement
` I,e, a = -kx `
But `a = nu (d nu )/(dx) :. (nu d nu)/(dx) = kx rArr int _(nu_1) ^(nu_2) nu d nu = - k int _(0) ^(x) xdx`
`(nu _(2)^(2) - nu_(1)^(2)) = - k (x^(2))/(2) `
`rArr (1)/(2) m (nu _(2)^(2) - nu_(1)^(2)) = (1)/(2) mk (9-x^(2))/(2)) `
:. Loss in kinetic energy `:. delta K prop x^(2) `