Initially spring is in natural length and both blocks are in rest condition. Then deter mine

maximum extension in spring . K = 20 N/M

Options

A. `(20)/(3)cm`
B. `(10)/(3)cm`
C. `(40)/(3)cm`
D. `(19)/(3) cm`

Answer

A

Explanation

`a=(F)/(m_(1)+m_(2))`
By work - energy theorem
`(F-m_(1)a) x_(1)+(m_(2)a)x_(2)-(1)/(2) k(x_(1)+x_(2))^(2)=0`
`m_(2)xx(F)/(m_(1)+m_(2)) (x_(1)+x_(2))=(K)/(2)(x_(1)+x_(2))^(2)`
`(x_(1) +x_(2))=m_(2) xx (F)/(m_(1)+m_(2)) xx (2)/(k)`
`=(1xx1)/(1.5) xx (2)/( 20) =(1)/(15)m=(100)/(15) cm=(20)/(3) cm`