Question

Two blocks $A\left(3kg\right)$ and $B\left(6kg\right)$ are connected by a spring of stiffness $512$ N/m and placed on a smooth horizontal surface. Initially the spring has its equilibrium length. Velocities $1.8$ m/s and $2.2$ m/s are imparted to A and B in opposite direction. The maximum extension in the spring will be?

• A. $25$ cm
• B. $10$ cm
• C. $12$ cm
• D. $2.5$ cm

Answer 1

The correct option is A $25$ cm

At maximum extension of the spring, velocities of both blocks will be same

Conservation of momentum:
6*2.2 – 3*1.8 = (3+6)*V
V = 0.867 m/s
Conservation of energy:
1/2*3*1.8*1.8 + 1/2*6*2.2*2.2 = 1/2*(6+3)*0.867*0.867 + 1/2*512* X*X
X = 0.25 m = 25 cm