Two blocks each of mass m are connected to a spring of spring constant k. if both are given velocity v in opposite directions, then the maximum elongation of the spring is

Options

A. `sqrt((mv^(2))/(k))`
B. `sqrt((2mv^(2))/(k))`
C. `sqrt((mv^(2))/(2k))`
D. `2sqrt((mv^(2))/(k))`

Answer

B

Explanation

Law of conservation of energy-
`(1)/(2) mv^(2)+(1)/(2)mv^(2)=(1)/(2)kx^(2)`
`implies mv^(2)=(1)/(2) kx^(2) implies x=sqrt((2mv^(2))/(k))`.