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Two blocks A and B of masses m & 2m plac...

Two blocks `A` and `B` of masses `m` & `2m` placed on smooth horizontal surface are connected with a light spring. The two blocks are given velocities as shown when spring is at natural length.
(i) Find velocity of centre of mass (b) maximum extension in the spring

Text Solution

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(a) `V_(CM)=(2mxx2v-m_(x)v)/(3m)=v`
(b) There will be maximum extension in spring when `v_(rel)=0`
`therefore` applying conservation of mechanical energy,
`(1)/(2)MV_(CM^(2))+0+(1)/(2)kx^(2)=(1)/(2)MV_(CM^(2))+(1)/(2)mu_(rel^(2))`
`x=sqrt((mu)/(k))v_(rel)=sqrt((2m)/(3k))xx3v=sqrt((6m)/(k))v`
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