Blocks A&B of mass m each are connected with spring of constant k both blocks lie on frictionless ground and are imparted horizontal velocity v as shown when spring is unstretched find the maximum stretch of spring.

Options

A. `vsqrt(m/k)`
B. `vsqrt(m/2k)`
C. `vsqrt(2m)/k`
D. none

Answer

A

Explanation

There is no change in velocity `bot` to the spring at the moment of maximum extension relative velocity along the spring is zero due to symmetry velocity of blocks is zero along spring at the moment of maximum extension

let extention be x Applying conservation of energy
`2[1/2m(v/sqrt(2))^(2)]+1/2kx^(2)=2(1/2mv^(2))`
`kx^(2)=mv^(2) Rightarrow x=v sqrt(m/k)`