Question

Two blocks `A` and `B` of mass `m` and `2m` respectively are connected by a massless spring of spring constant `K`. This system lies over a smooth horizontal surface. At `t=0` the bolck `A` has velocity u towards right as shown while the speed of block `B` is zero, and the length of spring is equal to its natural length at that at that instant.

`{:(,"Column I",,"Column II"),((A),"The velocity of block A",(P),"can never be zero"),((B),"The velocity of block B",(Q),"may be zero at certain instants of time"),((C),"The kinetic energy of system of two block",(R),"is minimum at maximum compression of spring"),((D),"The potential energy of spring",(S),"is maximum at maximum extension of spring"):}`

Answer 1

Correct Answer - (A) `rarr` p,r; (B) `rarr` q; (C ) `rarr` p,r; (D) `rarr` q,s
As no external force acts on the system velocity of centre of mass remain same

In frama of centre of mass velocity of B is `2u//3` and it oscillates from `(-(2u)/(3) (2u)/(3))`
In frame of centre of mass velocity of A is `u//3` and It oscillates from `(-(L)/(3), (u)/(3))`. In ground frame velocity of `B [0, (4u)/(3)]` , In ground frame velocity of `A [(u)/(3),u]` and by conservation of energy `DeltaK.E. = DeltaU_(s)`