Two blocks `A(3 kg)` and `B(2 kg)` resting on a smooth horizontal surface is connected by a spring of stiffness `480N//m`. Initially the spring is underformed and a velocity of `2 m//s` is imparted to A along the line of the spring away from B. The maximum extension in meters of the spring during subsequent motion is :-

Options

A. `(1)/(10)`
B. `(1)/(2sqrt10)`
C. `(1)/(2sqrt15)`
D. `0.15`

Answer

A

Explanation

`"COLM" : 3 xx 2 = (3 + 2) v rArr v = (6)/(5) m//s`
`"COME" : (1)/(2) xx 3 xx 2^(2) (1)/(2) xx 5 xx ((6)/(5))^(2) + (1)/(2) = 480 xx x^(2)`
`rArr x = (1)/(10)m`