Question

The system shown in the figure can move on a smooth surface. They are initially compressed by `6cm` and then released, then choose the correct options.

(a) The system performs, SHM with time period `(pi)/(10)s`
(b) The block of mass `3kg` perform SHM with amplitude `4 cm`
( c) The block of mass `6kg` will have maximum momentum of `2.40kg - m//s`
(d) The time periods of two blocks are in the ratio of `1:sqrt(2)`

Answer 1

Correct Answer - A
`mu =Reduced mass`
`=(m_(1)m_(2))/((m_(1)) + (m_(2))) = 2 kg`
`T = 2pi sqrt((mu)/(k))`
`= 2pi sqrt((2)/(800)) = (pi)/(10)s = T_(3) = T_(6)`
`A prop (1)/(m)`
`:. (A_(3))/(A_(6)) = (6)/(3) =(2)/(1)`
`:. A_(3) = 4cm` and `A_(6) = 2 cm`
`:. (P_(6))_(max) = m_(6) (v_(6))_(max)`
`= m_(6) (omega A_(6))`
`= (6)((2pi)/(pi//10)) (2xx10^(-2))`
`2.4 kg - m//s`
`:.` The correct option are (a, b, c).