Question

Two blocks of masses $3kg$ and $6kg$ rest on a horizontal smooth surface. The $3kg$ block is attached to a spring with a force constant $k=900N{m}^{-1}$ which is compressed $2m$ from the equilibrium position as shown in figure. The $6kg$ mass is at rest at $1m$ from mean position. $3kg$ mass strikes the $6kg$ mass and the two stick together :

• A. Velocity of the combined masses immediately after the collision is $10m{s}^{-1}$
• B. Velocity of the combined masses immediately after the collision is $5m{s}^{-1}$
• C. Amplitude of the resulting oscillation is $\sqrt{2}m$
• D. Amplitude of the resulting oscillation is $\sqrt{5/2}m$.

Answer 1

Answer: (A), (C)

When $3kg$ mass is released the amplitude of its oscillations is $2m$ and at a distance $1m$ from the equilibrium position we can find the speed of it using the relation $v={\left[(k/m)\left(A^2-x^2\right)\right]}^{1/2}$ then by conservation of momentum we can find the resulting speed of the combined mass and the new amplitude using the above relation