A particle is moving in a straight line with retardation proportional to its displacement.  Its loss of K.E for any displacement x is proportional to

detailed solution

Correct option is A

Given retardation α  displacement                    ∴     dvdt   α   x                  ⇒    dvdt    =   K x k is proportionlity constant                   ∴    dvdx ⋅ dxdt=   K ⋅x                         dvdx ⋅ V=   K ⋅x                   V  d  V  =    K⋅x⋅ dx                 v1v2∫vdv   =    K⋅ ax∫xdx                ∴      v222−v122  =    K⋅ x22              mv222−mv122  =    K⋅m2  x2             K.E2  −   K.E1  =    mKα ⋅  x2            ∴    loss  of  K.E α x2