The system shown in the figure can move on a smooth surface. The spring is initially compressed by 6 cm and then released.

Options

A. the particles perform SHM with time period `pi/10 sec`
B. the block of mass 3 kg perform SHM with amplitude 4 cm
C. the block of mass 6 kg will have maximum momentum `2.40 kg m//s`
D. none of these

Answer

A, B, C

Explanation

`pi/10-T=2/pisqrt((3xx6)/(9xxk)) Þ 1/10=2sqrt(2/k) Þ 1/100=2(2/k)`
`k=800`
`x_(1)+x_(2)=6Rightarrow3(x_(1))=6x_(2) Rightarrow x_(2)=2m,x_(1)=4cm`
`1/2kx^(2)=1/2m_(1)v_(1)^(2)+1/2m^(2)v_(2)^(2) Rightarrow m_(1)v_(1)=m_(2)v_(2)`
`3v_(1)=6v_(2) Rightarrow 1/2 xx800xx(6xx6)/(100xx100)=2.4`kgm//s