Two blocks `A (5 kg)` and `B( 5kg)` attached to the ends of a spring constant `1000 N//m` are placed on a smooth horizontal plane with the spring undeformed . Simultaneously velocities of `10m//s` and `4m//s` along the line of the spring in the same direction are imparted to` A` and `B` then

Options

A. When the extension of the spring is maximum the velocities of `A` and `B` are same.
B. the maximum extension of the spring is `30cm`.
C. the first maximum compression occurs `pi//56` seconds after start.
D. maximum compression and maxium extension occurs alternately.

Answer

A, B, D

Explanation

`(1)/(2)(m_(1)m_(2))/(m_(1)+m_(2))(V_(1)-V_(2))^(2)=(1)/(2)kx^(2)`
`(1)/(2)((5)(5))/(5+5)(10-4)^(2)=(1)/(2)xx1000x^(2)`
`2.5(36)=(1000)x^(2)`
`((25)(36)xx10^(-1))/(1000)=x^(2)`
`((25)(36))/(10000)=x^(2)`
`((5)(6))/(10)=x^(2)`
`x=0.30m`
Also `omega=sqrt((k)/(mu))=sqrt((1000)/(((5)(5))/(5+5)))`
`omega=20 sec. `
`T=(2pi)/(20)=(pi)/(10)`
The first maximum compression occurs `(T)/(4)=(pi)/(40)sec.` after start.