AB is a long frictionless horizontal surface. One end of an ideal spring of spring constant K is attached to a block of mass m, which is being moved left with constant velocity v, and the another end is free. Another block of mass 2m is given a velocity 3v towards the spring. Magnitude of work done by external agent in moving m with constant velocity v in long time is `beta` times `mv^(2)` . Find the value of `beta`

Explanation

Situation after long time

Work done `=DeltaK=1/2 (2m)(v^(2))-1/2 (2m)(3v)^(2)=mv^(2)-9m^(2)=-8 mv^(2)`.