A particle move in a straight line with retardation proportional to its displacement its loss of kinectic energy for any displacement `x` is proportional toA. xB. `e^(x)`C. `x^(2)`D. `log_(e) x`

A particle move in a straight line with retardation proportional to it

1.	A particle move in a straight line with retardation proportional to its displacement its loss of kinectic energy for any displacement `x` is proportional toA. xB. `e^(x)`C. `x^(2)`D. `log_(e) x`
Answer» Correct Answer - C According to problem Retardation `prop` displacement or `(dv)/(dt) = kx` or `v(dv)/(dt) = kx` or `vdv = kxdx` or `underset(v_(1)) overset(v_(2)) int vdv = underset(0) overset(x) int kdx` or `(v_(2)^(2))/(2) -(v_(1)^(2))/(2) =(kx^(2))/(2)` or `(1)/(m) ((mv_(2)^(2))/(2) -(mv_(1)^(2))/(2)) = (kx^(2))/(2)` or `(k_(2)-k_(1)) = (mk)/(2) x^(2)`. Thus, loss of kinetic enery is proportional to `x^(2)`.

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A particle move in a straight line with retardation proportional to its displacement its loss of kinectic energy for any displacement `x` is proportional toA. xB. `e^(x)`C. `x^(2)`D. `log_(e) x`

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