Question

As per the given figure, two blocks each of mass \(250\ g\) are connected to a spring of spring constant \(2\ Nm^{–1}\). If both are given velocity v in opposite directions, then maximum elongation of the spring is:

• A. \(\frac {v}{2\sqrt 2}\)
• B. \(\frac v2\)
• C. \(\frac v4\)
• D. \(\frac {v}{\sqrt 2}\)

Answer 1

The Correct Option is B

∵ Loss in Kinetic Energy = Gain in spring energy
\(⇒\frac 12mv^2×2=\frac 12kx_m^2\)
\(⇒2×\frac 14×v^2=2×x_m^2\)
\(⇒x_m=\sqrt {\frac {v^2}{4}}\)
\(⇒x_m=\frac v2\)

So, the correct option is (B): \(\frac v2\)