A spring of force constant k is kept in the compressesd conditionbetween two blocksmassesm and M on the smoothsurface of a table as shown in figure .When the springis released , both the blocksmove in oppositedirections .Whenthe springattainsthe orginal (normal ) position . both blockslose the constactswith the spring . If x is the intialcompressionof the springfind the speeds of blockwhilegettingdetached from the spring .

A spring of force constant k is kept in the compressesd conditionbetwe

1.	A spring of force constant k is kept in the compressesd conditionbetween two blocksmassesm and M on the smoothsurface of a table as shown in figure .When the springis released , both the blocksmove in oppositedirections .Whenthe springattainsthe orginal (normal ) position . both blockslose the constactswith the spring . If x is the intialcompressionof the springfind the speeds of blockwhilegettingdetached from the spring .
Answer» Solution :Suppose V and v be the velocity of the BLOCK of mass M and m respectively when they losethecontactwith spring. Here the initial momnetumis zero and finalmomentumis MV - mv Accordingto the lawof conservationof momentum ` MV - mv = 0 ` ` :. V = (mv)/M ` ` :. ` The potential energy stored in spring will be the intial ENERGYOF the system` = 1/2 kx^(2)` Final energy of the system` = 1/2 mv^(2) +1/2 Mv^(2)` (Neglecting FRICTIONAL forces ) ` :. 1/2 mv^(2)+1/2 Mv^(2)=1/2 kx^(2)` ` :. mv^(2) [1+m/M] =kx^(2)` ` :. mv^(2) [(M+m)/M] = kx^(2)` ` :. v^(2) = (KM)/(m(M+m)).x^(2)` ` :. v = x sqrt((kM)/(m(M+m)))`