A block C of mass m is moving with velocity v0 and collides elastically with block A of mass m and connected to another block B of mass 2m through spring of spring constant k. What is the value of k, if x0 is compression of spring, when velocity of A and B is same? [JIPMER 2017]

Using the law of conservation of linear momentum, we have                  mv0=mv + 2mv ⇒ v=v0/3Using law of conservation of energy, we have                     12mv02=12kx02+12(3m)v2where, x0 is compression in the spring.∴                 mv02=kx02+(3m)v029⇒                 kx02=mv02-mv023⇒kx02=2mv023∴                    k=2mv023x02